Diophantine m-tuples references (chronologically):

1. M. Gardner, Mathematical games, Scientific American 216 (1967), March 1967, p. 124; April 1967, p.119.

2. J. H. van Lint, On a set of diophantine equations, T. H.-Report 68 - WSK-03, Department of Mathematics, Technological University Eindhoven, Eindhoven, 1968.

3. A. Baker and H. Davenport, The equations 3x² - 2 = y² and 8x² - 7 = z², Quart. J. Math. Oxford Ser. (2) 20 (1969), 129-137.

4. P. Kanagasabapathy and T. Ponnudurai, The simultaneous Diophantine equations y² - 3x² = -2 and z² - 8x² = -7, Quart. J. Math. Oxford Ser. (2) 26 (1975), 275-278.

5. B. W. Jones, A variation on a problem of Davenport and Diophantus, Quart. J. Math. Oxford Ser. (2) 27 (1976), 349-353.

6. G. Sansone, Il sistema diofanteo N + 1 = x², 3N + 1 = y², 8N + 1 = z², Ann. Mat. Pura Appl. (4) 111 (1976), 125-151.

7. M. Gardner, Mathematical Magic Show, Alfred Knopf, New York, 1977, pp. 210, 221-222.

8. V. E. Hoggatt and G. E. Bergum, A problem of Fermat and the Fibonacci sequence, Fibonacci Quart. 15 (1977), 323-330.

9. G. Berzsenyi, Problem B-369, Fibonacci Quart. 16 (1978), 565.

10. P. E. Gibbs, Computer Bulletin 17 (1978), 16.

11. C. M. Grinstead, On a method of solving a class of Diophantine equations, Math. Comp. 32 (1978), 936-940.

12. B. W. Jones, A second variation on a problem of Diophantus and Davenport, Fibonacci Quart. 16 (1978), 155-165.

13. C. Leach, Computer Bulletin 15 (1978), 13.

14. J. Arkin, V. E. Hoggatt and E. G. Strauss, On Euler's solution of a problem of Diophantus, Fibonacci Quart. 17 (1979), 333-339.

15. P. Heichelheim, The study of positive integers (a,b) such that ab + 1 is a square, Fibonacci Quart. 17 (1979), 269-274.

16. J. Arkin, V. E. Hoggatt and E. G. Strauss, On Euler's solution of a problem of Diophantus II, Fibonacci Quart. 18 (1980), 170-176.

17. N. Thamotherampillai, The set of numbers {1,2,7}, Bull. Calcutta Math. Soc. 72 (1980), 195-197.

18. M. Veluppillai, The equations z² - 3y² = -2 and z² - 6x² = -5, A Collection of Manuscripts Related to the Fibonacci sequence, (V. E. Hoggatt, M. Bicknell-Johnson, eds.), The Fibonacci Association, Santa Clara}, 1980, pp. 71-75.

19. J. Morgado, Generalization of a result of Hoggatt and Bergum on Fibonacci numbers, Portugaliae Math. 42 (1983-1984), 441-445.

20. S. P. Mohanty and A. M. S. Ramasamy, The simultaneous Diophantine equations 5y² - 20 = x² and 2y² + 1 = z², J. Number Theory 18 (1984), 356-359.

21. E. Brown, Sets in which xy + k is always a square, Math. Comp. 45 (1985), 613-620.

22. H. Gupta and K. Singh, On k-triad sequences, Internat. J. Math. Math. Sci. 5 (1985), 799-804.

23. S. P. Mohanty and A. M. S. Ramasamy, The characteristic number of two simultaneous Pell's equations and its application, Simon Stevin 59 (1985), 203-214.

24. S. P. Mohanty and A. M. S. Ramasamy, On P_r,k sequences, Fibonacci Quart. 23 (1985), 36-44.

25. M. Nutt, Generalizations of Thamotherampillai's {1,2,7}, Bull. Calcuta Math. Soc. 78 (1986), 7-9.

26. A. F. Horadam, Generalization of a result of Morgado, Portugaliae Math. 44 (1987), 131-136.

27. J. Morgado, A problem concerning the Fibonacci numbers, Proceedings of the Second Meeting of Portuguese Algebraist, Univ. Porto, Porto, 1987, pp. 77-88 (in Portuguese).

28. D. X. Zheng, On the system of Diophantine equations y² - 2x² = 1, z² - 5x² = 4 and y² - 5x² = 4, z² - 10x² = 9, Sichuan Daxue Xuebao 24 (1987), 25-29 (in Chinese).

29. J. Arkin and G. E. Bergum, More on the problem of Diophantus, Application of Fibonacci Numbers, Vol. 2 (A. N. Philippou, A. F. Horadam, G. E. Bergum, eds.), Kluwer, Dordrecht, 1988, pp. 177-181.

30. G. Berzsenyi, Problems, puzzles, paradoxes, Consortium 25 (1988), 5.

31. C. Long and G. E. Bergum, On a problem of Diophantus, Application of Fibonacci Numbers, Vol 2 (A. N. Philippou, A. F. Horadam, G. E. Bergum, eds.), Kluwer, Dordrecht, 1988, pp. 183-191.

32. A. G. Shannon, Fibonacci numbers and Diophantine quadruples: Generalizations of results of Morgado and Horadam, Portugaliae Math. 45 (1988), 165-169.

33. V. K. Mootha and G. Berzsenyi, Characterization and extendibility of P_t-sets, Fibonacci Quart. 27 (1989), 287-288.

34. H. Altindis, Generalization of the set {1,2,5}, Istanbul Univ. Fen Fak. Mat. Derg. 49 (1990), 1-5.

35. J. H. Chen, Common solutions of the Pell equations x² - 2y² = 1 and y² - Dz² = 4, J. Wuhan Univ. Natur. Sci. Ed. (1990), 8-12.

36. A. Dujella, A problem of Diophantus and Fibonacci numbers, Matematika (Zagreb) 19 (3) (1990), 45-52 (in Croatian).

37. D. Zagier, Elliptische Kurven: Fortschritte und Anwendungen, Jahresber. Deutsch. Math.-Verein 92 (1990), 58-76.

38. G. Berzsenyi, Adventures among P_t-sets, Quantum 1 (4) (1991), 57.

39. J. Morgado, Note on a Shannon's theorem concerning the Fibonacci numbers and Diophantine quadruples, Portugaliae Math. 48 (1991), 429-439.

40. D. M. Bloom, Problem 10238, Amer. Math. Monthly 99 (1992), 674.

41. J. Roberts, Lure of the Integers, The Mathematical Association of America, 1992, pp. 31-35.

42. D. X. Zheng, On the system of Diophantine equations a₂x² - a₁y² = a₂ - a₁, a₃y² - a₂z² = a₃ - a₂, Sichuan Daxue Xuebao 29 (1992), 348-351 (in Chinese).

43. J. Arkin, D. C. Arney, F. R. Giordano, R. A. Kolb and G. E. Bergum, An extension of an old classical Diophantine problem, Application of Fibonacci Numbers, Vol. 5 (G. E. Bergum, A. N. Philippou, A. F. Horadam, eds.), Kluwer, Dordrecht, 1993, pp. 45-48.

44. A. Dujella, Generalization of a problem of Diophantus, Acta Arith. 65 (1993), 15-27.

45. H. Altindis, On P_2j sets, Bull. Calcuta Math. Soc. 86 (1994), 305-306.

46. G. Berzsenyi, Problem 4/14, Mathematics and Informatics Quarterly 5 (1995), 103-105.

47. R. Drnovsek, Solution of Problem 10238, Amer. Math. Monthly 102 (1995), 275-276.

48. A. Dujella, Diophantine quadruples for squares of Fibonacci and Lucas numbers, Portugaliae Math. 52 (1995), 305-318.

49. V. K. Mootha, On the set of numbers {14,22,30,42,90}, Acta Arith. 71 (1995), 259-263.

50. J. Morgado, Note on the Chebyshev polynomials and applications to the Fibonacci numbers, Portugaliae Math. 52 (1995), 363-378.

51. A. M. S. Ramasamy, A remarkable sequence, Banyan Mathematical Journal 2 (1995), 69-76.

52. Gh. Udrea, A problem of Diophantos-Fermat and Chebyshev polynomials of the second kind, Portugaliae Math. 52 (1995), 301-304.

53. Z. Y. Chen, The Diophantine system of equations 5x² - 3y² = 2, 16y² - 5z² = 11, J. Central China Normal Univ. Natur. Sci. 30 (1996), 381-384 (in Chinese).

54. M. N. Deshpande and G. E. Bergum, Interesting arrays associated with Fibonacci sequences, Applications of Fibonacci Numbers, Vol. 6 (G. E. Bergum, A. N. Philippou, A. F. Horadam, eds.), Kluwer, Dordrecht, 1996, pp. 85-92.

55. A. Dujella, Generalized Fibonacci numbers and the problem of Diophantus, Fibonacci Quart. 34 (1996), 164-175.

56. A. Dujella, Some polynomial formulas for Diophantine quadruples, Grazer Math. Ber. 328 (1996), 25-30.

57. A. Dujella, Generalization of the Problem of Diophantus and Davenport, Dissertation, University of Zagreb, 1996 (in Croatian).

58. S. T. Thakar, The role of "T" and "S" of IMTS, Mathematics and Informatics Quarterly 6 (1996), 23-26.

59. Gh. Udrea, A note on the sequence (W_n) of A. F. Horadam, Portugaliae Math. 53 (1996), 143-155.

60. Z. Y. Chen, Upper bounds for positive integer solutions of the indeterminate equations x² - 7y² = 2, z² - 32y² = -23, J. Central China Normal Univ. Natur. Sci. 31 (1997), 253-256 (in Chinese).

61. M. N. Deshpande, Problem 10622, Amer. Math. Monthly 104 (1997), 870.

62. A. Dujella, On Diophantine quintuples, Acta Arith. 81 (1997), 69-79.

63. A. Dujella, The problem of Diophantus and Davenport for Gaussian integers, Glas. Mat. Ser. III 32 (1997), 1-10.

64. A. Dujella, The problem of the extension of a parametric family of Diophantine triples, Publ. Math. Debrecen 51 (1997), 311-322.

65. A. Dujella, The problem of Diophantus and Davenport, Math. Commun. 2 (1997), 153-160.

66. M. N. Deshpande, One property of triangular numbers, Portugaliae Math. 55 (1998), 381-383.

67. A. Dujella, On the exceptional set in the problem of Diophantus and Davenport, Application of Fibonacci Numbers, Vol. 7 (G. E. Bergum, A. N. Philippou, A. F. Horadam, eds.), Kluwer, Dordrecht, 1998, pp. 69-76.

68. A. Dujella, A problem of Diophantus and Pell numbers, Application of Fibonacci Numbers, Vol. 7 (G. E. Bergum, A. N. Philippou, A. F. Horadam, eds.), Kluwer, Dordrecht, 1998, pp. 61-68.

69. A. Dujella, A problem of Diophantus and Dickson's conjecture, Number Theory, Diophantine, Computational and Algebraic Aspects (K. Gyory, A. Petho, V. T. Sos, eds.), Walter de Gruyter, Berlin, 1998, pp. 147-156.

70. A. Dujella, Some estimates of the number of Diophantine quadruples, Publ. Math. Debrecen 53 (1998), 177-189.

71. A. Dujella, Complete solution of a family of simultaneous Pellian equations, Acta Math. Inform. Univ. Ostraviensis 6 (1998), 59-67.

72. A. Dujella, Diophantine quadruples and quintuples modulo 4, Notes Number Theory Discrete Math. 4 (1998), 160-164.

73. A. Dujella and A. Petho, A generalization of a theorem of Baker and Davenport, Quart. J. Math. Oxford Ser. (2), 49 (1998), 291-306.

74. K. S. Kedlaya, When is (xy+1)(yz+1)(zx+1) a square?, Math. Mag. 71 (1998), 61-63.

75. K. S. Kedlaya, Solving constrained Pell equations, Math. Comp. 67 (1998), 833-842.

76. Z. Y. Chen, The system of Diophantine equations (m + 2)x² - my² = 2, (4m + 4)y² - (m + 2)z² = 3m + 2, J. Central China Normal Univ. Natur. Sci. 33 (1999), 1-5.

77. A. Dujella, A proof of the Hoggatt-Bergum conjecture, Proc. Amer. Math. Soc. 127 (1999), 1999-2005.

78. A. Dujella, An extension of an old problem of Diophantus and Euler, Fibonacci Quart. 37 (1999), 312-314.

79. Z. Franco, Solution of Problem 10622, Amer. Math. Monthly 106 (1999), 868.

80. P. Gibbs, A generalised Stern-Brocot tree from regular Diophantine quadruples, XXX Mathematics Archive math.NT/9903035.

81. E. Herrmann, A. Petho and H. G. Zimmer, On Fermat's quadruple equations, Abh. Math. Sem. Univ. Hamburg 69 (1999), 283-291.

82. L. Jones, A polynomial approach to a Diophantine problem, Math. Mag. 72 (1999), 52-55.

83. A. Petho, Algebraische Algorithmen, Vieweg, Braunschweig, 1999, pp. 106-115.

84. E. W. Weisstein, CRC Concise Encyclopedia of Mathematics, Chapman & Hall / CRC, Boca Raton, 1999, p. 759.

85. H. Widmer, Solution of Problem 10622, Amer. Math. Monthly 106 (1999), 867-868.

86. M. N. Deshpande, An interesting conjecture, The Mathematical Gazette 84 (2000), 296-298.

87. A. Dujella, Diophantine triples and construction of high-rank elliptic curves over with three non-trivial 2-torsion points, Rocky Mountain J. Math. 30 (2000), 157-164.

88. A. Dujella, A note on Diophantine quintuples, Algebraic Number Theory and Diophantine Analysis (F. Halter-Koch, R. F. Tichy, eds.), Walter de Gruyter, Berlin, 2000, pp. 123-127.

89. A. Dujella, A parametric family of elliptic curves, Acta Arith. 94 (2000), 87-101.

90. A. Dujella, Irregular Diophantine m-tuples and high-rank elliptic curves, Proc. Japan Acad. Ser. A Math. Sci. 76 (2000), 66-67.

91. A. Dujella and A. Petho, Integer points on a family of elliptic curves, Publ. Math. Debrecen 56 (2000), 321-335.

92. O. Kihel, On the extendibility of the P_-1-set {1,2,5}, Fibonacci Quart. 38 (2000), 464-466.

93. Gh. Udrea, A problem of Diophantus-Fermat and Chebyshev polynomials of the first kind, Rev. Roumaine Math. Pures Appl. 45 (2000), 531-535.

94. E. Assaf and S. Gueron, Characterization of regular Diophantine quadruples, Elem. Math. 56 (2001), 71-81.

95. M. N. Deshpande and E. Brown, Diophantine triplets and the Pell sequence, Fibonacci Quart. 39 (2001), 242-249.

96. A. Dujella, An absolute bound for the size of Diophantine m-tuples, J. Number Theory 89 (2001), 126-150.

97. A. Dujella, Diophantine m-tuples and elliptic curves, J. Theor. Nombres Bordeaux 13 (2001), 111-124.

98. P. Gibbs, Diophantine quadruples and Cayley's hyperdeterminant, XXX Mathematics Archive math.NT/0107203

99. K. Gyarmati, On a problem of Diophantus, Acta Arith. 97 (2001), 53-65.

100. K. Gyarmati, Powers, powerful and powerfree numbers in sumsets and multiplicative structures, Master Thesis, Eotvos University, Budapest, 2001 (in Hungarian).

101. A. Kihel and O. Kihel, Sets in which the product of any k elements increased by t is a kth-power, Fibonacci Quart. 39 (2001), 98-100.

102. A. Kihel and O. Kihel, On the intersection and the extendability of P_t sets, Far East J. Math. Sci. 3 (2001), 637-643.

103. A. F. Beardon and M. N. Deshpande, Diophantine triples, The Mathematical Gazette 86 (2002), 258-260.

104. M. N. Deshpande, One interesting family of diophantine triplets, Internat. J. Math. Ed. Sci. Tech. 33 (2002), 253-256.

105. M. N. Deshpande, A problem in number theory, Resonance 7(7) (2002), 89-91.

106. M. N. Deshpande and A. Dujella, An interesting property of a reccurence related to the Fibonacci sequence, Fibonacci Quart. 40 (2002), 157-160.

107. A. Dujella, On the size of Diophantine m-tuples, Math. Proc. Cambridge Philos. Soc. 132 (2002), 23-33.

108. A. Dujella, An extension of an old problem of Diophantus and Euler. II, Fibonacci Quart. 40 (2002), 118-123.

109. A. Dujella, C. Fuchs and R. F. Tichy, Diophantine m-tuples for linear polynomials, Period. Math. Hungar. 45 (2002), 21-33.

110. C. Fuchs, Quantitative finiteness results for Diophantine equations, Dissertation, TU Graz, 2002.

111. K. Gyarmati, A. Sarkozy and C. L. Stewart, On shifted products which are powers, Mathematika 49 (2002), 227-230.

112. M. J. Jacobson, Jr. and H. C. Williams, Modular arithmetic on elements of small norm in quadratic fields, Des. Codes and Cryptogr. 27 (2002), 93-110.

113. Y. Bugeaud and A. Dujella, On a problem of Diophantus for higher powers, Math. Proc. Cambridge Philos. Soc. 135 (2003), 1-10.

114. M. N. Deshpande, Families of Diophantine triplets, Bulletin of the Marathwada Mathematical Society 4 (2003), 19-21.

115. A. Dujella and C. Fuchs, A polynomial variant of a problem of Diophantus and Euler, Rocky Mountain J. Math. 33 (2003), 797-811.

116. F. S. Abu Muriefah and A. Al- Rashed, On the exendibility of the Diophantine triple {1,5,c}, Internat. J. Math. Math. Sci. 33 (2004), 1737-1746.

117. F. S. Abu Muriefah and A. Al- Rashed, Some Diophantine quadruples in the ring Z[√-2], Math. Commun. 9 (2004), 1-8.

118. J. Almeida and A. Machiavelo, Jose Morgado, Bulletin of International Center for Mathematics 17 (2004), 24-27.

119. J. Almeida and A. Machiavelo, Jose Morgado: in memoriam, Boletim da SPM 50 (2004), 1-18.

120. Y. Bugeaud, On the Diophantine equation (x^k-1)(y^k-1) = (z^k-1), Indag. Math. 15 (2004), 21-28.

121. Y. Bugeaud and K. Gyarmati, On generalizations of a problem of Diophantus, Illinois J. Math. 48 (2004), 1105-1115.

122. A. Dujella, There are only finitely many Diophantine quintuples, J. Reine Angew. Math. 566 (2004), 183-214.

123. A. Dujella, Bounds for the size of sets with the property D(n), Glas. Mat. Ser. III 39 (2004), 199-205.

124. A. Dujella, Diophantine quadruples and Fibonacci numbers, Bulletin of Kerala Mathematical Association 1 (2004), 133-147.

125. A. Dujella and C. Fuchs, Complete solution of the polynomial version of a problem of Diophantus, J. Number Theory 106 (2004), 326-344.

126. Z. Franusic, Diophantine quadruples in the ring Z[√2], Math. Commun. 9 (2004), 141-148.

127. R. K. Guy, Unsolved Problems in Number Theory, 3rd edition, Springer-Verlag, New York, 2004, Section D29, p. 310.

128. D. Saraswathy, A Study on Sets of Numbers with Diophantine Property, M.Phil. Dissertation, Department of Mathematics, Pondicherry University, Pondicherry, 2004.

129. M. Waldschmidt, Open Diophantine problems, Moscow Math. J. 4 (2004), 245-305.

130. R. Dietmann, C. Elsholtz, K. Gyarmati and M. Simonovits, Shifted products that are coprime pure powers, J. Combin. Theory Ser. A 111 (2005), 24-36.

131. A. Dujella and C. Fuchs, Complete solution of a problem of Diophantus and Euler, J. London Math. Soc. 71 (2005), 33-52.

132. A. Dujella and F. Luca, Diophantine m-tuples for primes, Int. Math. Res. Not. 47 (2005), 2913-2940.

133. A. Dujella and A. M. S. Ramasamy, Fibonacci numbers and sets with the property D(4), Bull. Belg. Math. Soc. Simon Stevin 12 (2005), 401-412.

134. A. Filipin, Non-extendibility of D(-1)-triples of the form {1,10,c}, Internat. J. Math. Math. Sci. 35 (2005) 2217-2226.

135. Z. Franusic, Diophantine Quadruples in Quadratic Fields, Dissertation, University of Zagreb, 2005 (in Croatian).

136. C. Fuchs, Upper Bounds for the Solutions of Diophantine Problems, Habilitation Thesis, TU Graz, 2005.

137. K. Gyarmati, A polynomial extension of a problem of Diophantus, Publ. Math. Debrecen 66 (2005), 389-405.

138. F. Luca, On shifted products which are powers, Glas. Mat. Ser. III 40 (2005), 13-20.

139. F. S. Abu Muriefah and A. Al- Rashed, On the simultaneous Diophantine equations y² - 5x² = 4 and z² - 442x² = 441, Arab. J. Sci. Eng. Sect. A Sci. 31 (2006) 207-211.

140. A. Dujella, C. Fuchs and P. G. Walsh, Diophantine m-tuples for linear polynomials. II. Equal degrees, J. Number Theory 120 (2006), 213-228.

141. A. Filipin, Systems of Pellian Equations and the Problem of Extension of Some Diophantine Triples, Dissertation, University of Zagreb, 2006 (in Croatian).

142. Y. Fujita, The unique representation d = 4k(k² - 1) in D(4)-quadruples {k-2, k+2, 4k, d}, Math. Commun. 11 (2006), 69-81.

143. Y. Fujita, The non-extensibility of D(4k)-triples {1, 4k(k-1), 4k²+1} with |k| prime, Glas. Mat. Ser. III 41 (2006), 205-216.

144. P. Gibbs, Some rational Diophantine sextuples, Glas. Mat. Ser. III 41 (2006), 195-203.

145. P.-C. Hu, C.-C. Yang, Value Distribution Theory Related to Number Theory, Birkhäuser, Basel, 2006, pp. 335-336.

146. Y. Li, An upper bound for the positive integer solutions of the system of Diophantine equations 7x²-5y²=2, 24y²-7z²=17, J. Chongqing Norm. Univ. Nat. Sci. Ed. 23 (2006), 33-35. (in Chinese).

147. A. Silvester, Fast and Unconditional Principal Ideal Testing, Master's thesis, University of Calgary, 2006.

148. Y. Bugeaud, A. Dujella, M. Mignotte, On the family of Diophantine triples {k - 1, k + 1, 16k^3 - 4k}, Glasgow Math. J. 49 (2007), 333-344.

149. A. Dujella, On Mordell-Weil groups of elliptic curves induced by Diophantine triples, Glas. Mat. Ser. III 42 (2007), 3-18.

150. A. Dujella, A. Filipin and C. Fuchs, Effective solution of the D(-1)-quadruple conjecture, Acta Arith. 128 (2007), 319-338.

151. A. Dujella and F. Luca, On a problem of Diophantus with polynomials, Rocky Mountain J. Math. 37 (2007), 131-157.

152. A. Filipin, Extensions of some parametric families of D(16)-triples, Internat. J. Math. Math. Sci. 2007 (2007), Article ID 63739, 12 pages

153. Y. Fujita, The extensibility of D(-1)-triples {1,b,c}, Publ. Math. Debrecen 70 (2007), 103-117.

154. Y. Fujita, The D(1)-extensions of D(-1)-triples {1, 2, c} and integer points on the attached elliptic curves, Acta Arith. 128 (2007), 349-375.

155. K. Gyarmati and C. L. Stewart, On powers in shifted products, Glas. Mat. Ser. III 42 (2007), 273-279.

156. T. Liqun, On the property P_-1, Integers 7 (2007), #A47

157. K. Kaygisiz and H. Senay, Constructions of some new nonextandable P_k sets, International Mathematical Forum 2 (2007), 2869-2874.

158. A. M. S. Ramasamy, Sets and sequences linked with a question of Diophantus, Bulletin of Kerala Mathematics Association 4 (2007), 109-125.

159. M. N. Deshpande, Diophantine triples from recurrence relations, preprint.

160. A. Dujella, On the number of Diophantine m-tuples, Ramanujan J. 15 (2008), 37-46.

161. A. Dujella, C. Fuchs and F. Luca, A polynomial variant of a problem of Diophantus for pure powers, Int. J. Number Theory 4 (2008), 57-71.

162. A. Dujella and V. Petricevic, Strong Diophantine triples, Experiment. Math. 17 (2008), 83-89.

163. A. Filipin, On the size of sets in which xy + 4 is always a square, Rocky Mountain J. Math. 39 (2009), 1195-1224.

164. A. Filipin, There does not exist a D(4)-sextuple, J. Number Theory 128 (2008), 1555-1565.

165. A. Filipin and Y. Fujita, Any polynomial D(4)-quadruple is regular, Math. Commun. 13 (2008), 45-55.

166. Z. Franusic, Diophantine quadruples in Z[√(4k+3)], Ramanujan J. 17 (2008), 77-88.

167. Z. Franusic, A Diophantine problem in Z[(1+√d)/2], Studia Sci. Math. Hungar. 46 (2009), 103-112.

168. Y. Fujita, The extensibility of Diophantine pairs {k-1, k+1}, J. Number Theory 128 (2008), 322-353.

169. Y. Fujita, The Hoggatt-Bergum conjecture on D(-1)-triples {F_2k+1, F_2k+3, F_2k+5} and integer points on the attached elliptic curves, Rocky Mountain J. Math. 39 (2009), 1907-1932.

170. C. L. Stewart, On sets of integers whose shifted products are powers, J. Combin. Theory Ser. A 115 (2008), 662-673.

171. G. Campbell and E. H. Goins, Heron triangles, Diophantine problems and elliptic curves, preprint.

172. Y. Fujita, Any Diophantine quintuple contains a regular Diophantine quadruple, J. Number Theory 129 (2009), 1678-1697.

173. Y. Fujita, The number of Diophantine quintuples, Glas. Mat. Ser. III 45 (2010), 15-29.

174. A. J. MacLeod, Square Eulerian quadruples, Rad Hrvat. Akad. Znan. Umjet. Mat. Znan. 20 (2016), 1-7.

175. D. S. Nagaraj and P. Shastri, On the determination of Diophantine triples, in: Number Theory and Applications (S. D. Adhikari, B. Ramakrishnan, eds.), Hindustan Book Agency, 2009, pp. 139-148.

176. R. Tamura, Non-extendibility of D(-1)-triples {1,b,c}, preprint.

177. C. Fuchs, F. Luca and L. Szalay, Diophantine triples with values in binary recurrences, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 7 (2008), 579-608.

178. F. Luca and L. Szalay, Fibonacci Diophantine triples, Glas. Mat. Ser. III 43 (2008), 253-264.

179. K. Kaygisiz, H. Senay and N. Bircan, Construction of some new nonextended P_k sets, preprint.

180. A. Dujella, Conjectures and results on the size and number of Diophantine tuples, Diophantine Analysis and Related Fields (DARF 2007/2008), AIP Conf. Proc. 976 (T. Komatsu, ed.), Amer. Inst. Phys., Melville, NY, 2008, pp. 58-61.

181. Y. Fujita, Diophantine quadruples containing some triples and the number of Diophantine quintuples, Diophantine Analysis and Related Fields (DARF 2007/2008), AIP Conf. Proc. 976 (T. Komatsu, ed.), Amer. Inst. Phys., Melville, NY, 2008, pp. 90-95.

182. Z. Franusic, On the extensibility of Diophantine triples {k-1, k+1, 4k} for Gaussian integers, Glas. Mat. Ser. III 43 (2008), 265-291.

183. J.-M. de Koninck and A. Mercier, 1001 Problems in Classical Number Theory, American Mathematical Society, Providence, 2007, pp. 284-285.

184. F. Najman, Compact representation of quadratic integers and integer points on some elliptic curves, Rocky Mountain J. Math. 40 (2010), 1979-2002.

185. A. Filipin, An irregular D(4)-quadruple cannot be extended to a quintuple, Acta Arith. 136 (2009), 167-176.

186. F. Najman, Integer points on two families of elliptic curves, Publ. Math. Debrecen 75 (2009), 401-418.

187. A. Dujella, Rational Diophantine sextuples with mixed signs, Proc. Japan Acad. Ser. A Math. Sci. 85 (2009), 27-30.

188. Bo He and A. Togbé, On the family of Diophantine triples {k+1, 4k, 9k+3}, Period. Math. Hungar. 58 (2009), 59-70.

189. Bo He and A. Togbé, On a family of Diophantine triples {k, A²k+2A, (A+1)²k+2(A+1)} with two parameters, Acta Math. Hungar. 124 (2009), 99-113.

190. A. Filipin, There are only finitely many D(4)-quintuples, Rocky Mountain J. Math. 41 (2011), 1847-1860.

191. A. Filipin and A. Togbé, On the family of Diophantine triples {k+2, 4k, 9k+6}, Acta Math. Acad. Paedagog. Nyhazi. 25 (2009), 145-153.

192. F. Luca and L. Szalay, Lucas Diophantine triples, Integers 9 (2009), #A35, 441-457.

193. S.-C. Yang, On the solutions of the Pell Equations x²-7y²=2, 32y²-z²=23, Journal of Tianzhong 22 (2007). (in Chinese).

194. W. D. Banks, F. Luca and L. Szalay, A variant on the notion of a diophantine s-tuple, Glasgow Math. J. 51 (2009), 83-89.

195. G. Martin and S. Sitar, Erdös-Turán with a moving target, equidistribution of roots of reducible quadratics, and Diophantine quadruples, Mathematika 57 (2011), 1-29.

196. A. Dujella and A. Jurasic, On the size of sets in a polynomial variant of a problem of Diophantus, Int. J. Number Theory 6 (2010), 1449-1471.

197. H. Balasunderam, The set of numbers {1, 5, 10}, J. Natn. Sci. Coun. Sri Lanka 6 (1978), 23-26.

198. P. Gibbs, Adjugates of Diophantine quadruples, Integers 10 (2010), 201-209.

199. A. Dujella and I. Soldo, Diophantine quadruples in Z[√-2], An. Stiint. Univ. "Ovidius" Constanta Ser. Mat. 18 (2010), 81-98.

200. J.-M. de Koninck, Those Fascinating Numbers, American Mathematical Society, Providence, 2009, p. 120.

201. A. Filipin, On the polynomial parametric family of the sets with the property D(-1;1), Bol. Soc. Mat. Mexicana 16 (2010), 1-8.

202. Y. Fujita, Extensions of the D(∓k²)-triples {k², k² ± 1, 4k² ± 1}, Period. Math. Hungar. 59 (2009), 21-33.

203. A. Filipin, Bo He and A. Togbé, On a family of two-parametric D(4)-triples, Glas. Mat. Ser. III 47 (2012), 31-51.

204. A. Filipin, Bo He and A. Togbé, On the D(4)-triple { F_2k, F_2k+6, 4F_2k+4 }, Fibonacci Quart. 48 (2010), 219-227.

205. A. Filipin, Y. Fujita, The number of D(-1)-quadruples, Math. Commun. 15 (2010), 387-391.

206. H. Hemme, Mathematik zum Frühstück. 89 mathematische Rätsel mit ausführlichen Lösungen, Vandenhoeck & Ruprecht, Göttingen, 1990, p. 40, 130.

207. B. Sriraman, H. Adrian, The existential void in learning: Juxtaposing mathematics and literature, in: Interdisciplinarity, Creativity, and Learning (B. Sriraman, V. Freiman, N. Lirette-Pitre, eds.), Age Publishing, 2009, pp. 13-29.

208. T. Koshy, Fibonacci and Lucas Numbers with Applications, Wiley, New York, 2001, pp. 93-95.

209. J. Aguirre, A. Dujella, J. C. Peral, On the rank of elliptic curves coming from rational Diophantine triples, Rocky Mountain J. Math. 42 (2012), 1759-1776.

210. Bo He and A. Togbé, On a family of Diophantine triples {k, A²k+2A, (A+1)²k+2(A+1)} with two parameters II, Period. Math. Hungar. 64 (2012), 1-10.

211. Z. Cerin, G. M. Gianella, On Diophantine triples from Pell and Pell-Lucas numbers, Atti Accad. Sci. Torino Cl. Sci. Fis. Mat. Natur. 143 (2009), 83-94.

212. Z. Y. Chen, The system of Diophantine equations 9x² - 7y² = 2, 32y² - 9z² = 23, J. Central China Normal Univ. Natur. Sci. 30 (1996), 24-28 (in Chinese).

213. Z. S. Zheng, On an upper bound for the positive integer solutions of the system of Diophantine equations 11x² - 9y² = 2, 40y² - 11z² = 29, Math. Practice Theory 38 (2008), 210-214 (in Chinese).

214. Y. Li, An upper bound for the positive integer solutions of the system of Diophantine equations 6x²-4y²=2, 20y²-6z²=14, J. Chongqing Norm. Univ. Nat. Sci. Ed. 24 (2009), 19-21 (in Chinese).

215. A. Filipin, Y. Fujita, The D(-k²)-triple {1,k²+1,k²+4} with k prime, Glas. Mat. Ser. III 46 (2011), 311-323.

216. M. N. Deshpande, Problem 94.C, The Mathematical Gazette 94 (2010), 159.

217. Z. Cerin, G. M. Gianella, On D(-4) and D(8) triples from Pell and Pell-Lucas numbers, Rend. Circ. Mat. Palermo (2) Suppl. 81 (2009), 73-83.

218. Y. Fujita, A. Togbé, The extension of the D(-k²)-pair {k², k² + 1}, Period. Math. Hungar. 65 (2012), 75-81.

219. G. N. Özcan, Diophantine Quadruples and Generalized Bivariate Polynomial Sequences, M. Sc. Thesis, Selcuk University, Konya, 2009 (in Turkish).

220. A. Nalli, G. N. Özcan, Generalized bivariate polynomials and Diophantine quadruples, preprint.

221. H. Altindis, Characterization and extendability of P_k sets for k ≡ 3(4), Gazi University Journal of Science 23 (2010), 295-297.

222. A. Jurasic, Diophantine m-tuples for quadratic polynomials , Glas. Mat. Ser. III 46 (2011), 283-309.

223. Bo He, A. Togbé, On the D(-1)-triple {1,k²+1,k²+2k+2} and its unique D(1)-extension, J. Number Theory 131 (2011), 120-137.

224. R. Esdahl-Schou, Diophantine tuple, Student project, University of Aarhus, 2009.

225. F. Najman, Compact Representation of Quadratic Integers and Integer Points on Elliptic Curves, Dissertation, University of Zagreb, 2010 (in Croatian).

226. A. Jurasic, Polinomial Variants of a Problem of Diophantus, Dissertation, University of Zagreb, 2010 (in Croatian).

227. Z. Franusic, On the extension of the Diophantine pair {1,3} in Z[√d], J. Integer Seq. 13 (2010), Article 10.9.6

228. P. Corvaja, U. Zannier, An abcd Theorem over function fields and applications, Bull. Soc. Math. France 139 (2011), 437-454.

229. A. Filipin, Y. Fujita, M. Mignotte, The non-extendibility of some parametric families of D(-1)-triples, Q. J. Math. 63 (2012), 605-621.

230. A. Bérczes, A. Dujella, L. Hajdu and F. Luca, On the size of sets whose elements have perfect power n-shifted products, Publ. Math. Debrecen 79 (2011), 325-339.

231. L. Bapoungue, The system of Diophantine equations 7z² - 20y² = -52 and 3z² -20x² = -68, Internat. J. Algebra, Number theory and Applications, 1 (2009), 1-11.

232. A. Dujella, A. Jurasic, Some Diophantine triples and quadruples for quadratic polynomials, J. Comb. Number Theory 3(2) (2011), 123-141.

233. S. Prugsapitak, V. Laohakosol, Some families of Diophantine quadruples, ScienceAsia 37 (2011), 152-159.

234. N. C. Bonciocat, M. Cipu, M. Mignotte, On D(-1)-quadruples, Publ. Mat. 56 (2012), 279-304.

235. A. Filipin, Y. Fujita, The number of Diophantine quintuples II, Publ. Math. Debrecen 82 (2013), 293-308.

236. W. Narkiewicz, Teoria liczb w tworczosci Eulera, Wiadom. Mat. 43 (2007), 87-98.

237. A. Filipin, Y. Fujita, The relative upper bound for the third element in a D(-1)-quadruple, Math. Commun. 17 (2012), 13-19.

238. A. Dujella and C. Fuchs, On a problem of Diophantus for rationals, J. Number Theory 132 (2012), 2075-2083.

239. Z. Cerin, G. M. Gianella, Matrices with rows in Euler triples from Pell and Pell-Lucas numbers, JP J. Algebra Number Theory Appl. 21 (2011), 117-132.

240. Z. Cerin, Determinants and permanents of matrices from Fibonacci and Lucas numbers, Pioneer Journal of Algebra, Number Theory and its Applications 1 (2011), 9-22.

241. Z. Franusic, D. Kreso, Nonextensibility of the pair {1,3} to a Diophantine quintuple in Z[√-2], J. Comb. Number Theory 3(3) (2011), 1-15.

242. M. N. Deshpande, Problem B-1073, Fibonacci Quart. 48 (2010), 278.

243. B. P. Beasley, Solution of Problem B-1073, Fibonacci Quart. 49 (2011), 276-277.

244. Z. Cerin, Squares from D(-4) and D(20) triples, Advances in Pure Mathematics 1 (2011), 286-294.

245. W. Narkiewicz, Rational Number Theory in the 20th Century. From PNT to FLT, Springer, London, 2012, Section 6.6.4, pp. 351-352.

246. A. Nowicki, Podroze po Imperium Liczb, 03 Liczby Kwadratowe, Wydawnictwo OWSIiZ, Olsztyn, 2009, Chapter 6, pp. 87-97.

247. A. M. S. Ramasamy, D. Saraswathy, A non-extendable Diophantine quadruple arising from a triple of Lucas numbers, Involve 5 (2012), 257-271.

248. Y. Fujita, A. Togbé, Uniqueness of the extension of the D(4k²)-triple {k² - 4, k², 4k² - 4}, Notes Number Theory Discrete Math. 17(4) (2011), 42-49.

249. L. Szalay, V. Ziegler, On an S-unit variant of Diophantine m-tuples, Publ. Math. Debrecen 83 (2013), 97-121.

250. Z. Cerin, Pencils of Euler triples, I, Sarajevo J. Math. 8 (2012), 15-31.

251. Z. Cerin, On extended Euler quadruples, Atti Semin. Mat. Fis. Univ. Modena Reggio Emilia 58 (2011), 101-120.

252. Y. Zhang, Diophantine triples and extendibility of {1,2,5} and {1,5,10}, Master Thesis, Central Michigan University, 2011.

253. W. Rich, Regular Diophantine m-tuples and their extensions, PhD Thesis, Central Michigan University, 2012.

254. Z. Cerin, Pencils of Euler triples, II, Sarajevo J. Math. 8 (2012), 179-192.

255. Lj. Jukic Matic, Non-existence of certain Diophantine quadruples in rings of integers of pure cubic fields, Proc. Japan Acad. Ser. A Math. Sci. 88 (2012), 163-167.

256. A. Ipek, On algebraic properties of the generalized Chebyshev polynomials, Transylv. J. Math. Mech. 2 (2010), 59-66.

257. Lj. Bacic, A. Filipin, On the family of D(4)-triples {k - 2, k + 2, 4k³ - 4k}, Bull. Belg. Math. Soc. Simon Stevin 20 (2013), 777-787.

258. Lj. Bacic, A. Filipin, On the extendibility of D(4)-pair {k - 2, k + 2}, J. Comb. Number Theory 5 (2013), 181-197.

259. A. Filipin, Y. Fujita, A. Togb´e, The extendibility of Diophantine pairs I: the general case, Glas. Mat. Ser. III 49 (2014), 25-36.

260. I. Soldo, On the existence of Diophantine quadruples in Z[√-2], Miskolc Math. Notes 14 (2013), 265-277.

261. I. Soldo, On the extensibility of D(-1)-triples {1, b, c} in the ring Z[√-t], t > 0, Studia Sci. Math. Hungar. 50 (2013), 296-330.

262. H. Lao, On the number of Diophantine m-tuples, Adv. Math. (China) 39 (2010), 277-282.

263. A. Dujella and J. C. Peral, High rank elliptic curves with torsion Z/2Z × Z/4Z induced by Diophantine triples, LMS J. Comput. Math. 17 (2014), 282-288.

264. M. Alp, N. Irmak, L. Szalay, Balancing diophantine triples, Acta Univ. Sapientiae Math. 4 (2012), 11-19.

265. K. R. Matthews, J. P. Robertson, J. White, On a Diophantine equation of Andrej Dujella, Glas. Mat. Ser. III 48 (2013), 265-289.

266. F. Luca, L. Szalay, On the Fibonacci distances of ab, ac and bc, Ann. Math. Inform. 41 (2013), 137-163.

267. A. Dujella, N. Saradha, Diophantine m-tuples with elements in arithmetic progressions, Indag. Math. (N.S.) 25 (2014), 131-136.

268. A. Dujella, M. Mikic, On the torsion group of elliptic curves induced by D(4)-triples, An. Stiint. Univ. "Ovidius" Constanta Ser. Mat. 22 (2014), 79-90.

269. Z. Franusic, Diophantine quadruples in the ring of integers of Q( ³√2), Miskolc Math. Notes 14 (2013), 893-903.

270. Lj. Jukic Matic, On D(w)-quadruples in the rings of integers of certain pure number fields, Glas. Mat. Ser. III 49 (2014), 37-46.

271. C. Elsholtz, A. Filipin, Y. Fujita, On Diophantine quintuples and D(-1)-quadruples, Monatsh. Math. 175 (2014), 227-239.

272. L. Szalay, V. Ziegler, S-Diophantine quadruples with two primes congruent 3 modulo 4, Integers 13 (2013), #A80.

273. A. Srinivasan, On the prime divisors of elements of a D(-1) quadruple, Glas. Mat. Ser. III 49 (2014), 275-285.

274. Lj. Bacic, A. Filipin, The extendibility of D(4)-pairs, Math. Commun. 18 (2013), 447-456.

275. Z. Cerin, Squares in Euler triples from Fibonacci and Lucas numbers, Cubo 15 (2013), 79-88.

276. M. Mikic, On the Mordell-Weil group of elliptic curves induced by the families of Diophantine triples, Rocky Mountain J. Math. 45 (2015), 1565-1589.

277. J. McLean, P_k-sets, Mathematical Spectrum 24 (1992), 78-79.

278. W. Wu and Bo He, On Diophantine quintuple conjecture, Proc. Japan Acad. A Math. Sci. 90 (2014), 84-86.

279. I. Soldo, D(-1)-triples of the form {1, b, c} in the ring Z[√-t], t > 0, Bull. Malays. Math. Sci. Soc. (2) 39 (2016), 1201-1224.

280. G. Srividhya, Diophantine quadruples for Fibonacci numbers with property D(1), Indian Journal of Mathematics and Mathematical Sciences 5 (2009), 57-59.

281. M. A. Gopalan, V. Pandichelvi, On the extendibility of the Diophantine triple involving Jacobsthal numbers (J_2n-1, J_2n+1 - 3, 2J_2n + J_2n-1 + J_2n+1 - 3), International Journal of Mathematics & Applications 2 (2009), 1-3.

282. V. Pandichelvi, Construction of the Diophantine triple involving polygonal numbers, Impact J. Sci. Tech. 5 (2011), 7-11.

283. M. A. Gopalan, G. Srividhya, Diophantine quadruples for Fibonacci and Lucas numbers with property D(4), Diophantus J. Math. 1 (2012), 15-18.

284. M. A. Gopalan, G. Srividhya, Some non-extendable P_-5 sets, Diophantus J. Math. 1 (2012), 19-22.

285. M. A. Gopalan, G. Srividhya, Two special Diophantine triples, Diophantus J. Math. 1 (2012), 23-27.

286. M. A. Gopalan, V. Sangeetha, M. Somanath, Construction of the Diophantine triple involving polygonal numbers, Sch. J. Eng. Tech. 2 (2014), 19-22.

287. B. Peker, A. Dujella, S. Cenberci, The non-extensibility of D(-2k+1)-triples {1, k², k²+2k-1}, Miskolc Math. Notes 16 (2015), 385-390.

288. F. Luca, V. Ziegler, A note on the number of S-Diophantine quadruples, Commun. Math. 22 (2014), 49-55.

289. K. S. Bhanu, M. N. Deshpande, Interesting dates, Mathematics in School 44 (2015), 37.

290. L. Szalay, V. Ziegler, S-Diophantine quadruples with S = {2, q}, Int. J. Number Theory 11 (2015), 849-868.

291. K. Meena, S. Vidhyalakshmi, M. A. Gopalan, G. Akila, R. Presenna, Formation of special Diophantine quadruples with property D(6kpq)², The International Journal of Science & Technoledge 2 (2014), 11-14.

292. M. A. Gopalan, S. Vidhyalakshmi, S. Mallika, Some special non-extendable Diophantine triples, Sch. J. Eng. Tech. 2 (2014), 159-160.

293. C. A. Gomez Ruiz, F. Luca, Tribonacci Diophantine quadruples, Glas. Mat. Ser. III 50 (2015), 17-24.

294. M. A. Gopalan, S. Vidhyalakshmi, E. Premalatha, K. Presenna, On the extendibility of 2-tuple to 4-tuple with property D(4), Bulletin of Mathematical Sciences & Applications 3 (2014), 100-104.

295. Lj. Bacic, A. Filipin, A note on the number of D(4)-quintuples, Rad Hrvat. Akad. Znan. Umjet. Mat. Znan. 18 (2014), 7-13.

296. Z. Franusic, I. Soldo, The problem of Diophantus for integers of Q(√-3), Rad Hrvat. Akad. Znan. Umjet. Mat. Znan. 18 (2014), 15-25.

297. S. Vidhyalakshmi, M. A. Gopalan, K. Lakshmi, Gaussian - Diophantine quadruples with property D(1), IOSR Journal of Mathematics 10 (2014), 12-14.

298. M. Cipu, Y. Fujita, Bounds for Diophantine quintuples, Glas. Mat. Ser. III 50 (2015), 25-34.

299. A. Filipin, Y. Fujita, A. Togbé, The extendibility of Diophantine pairs II: examples, J. Number Theory 145 (2014), 604-631.

300. A. Filipin, The extendibility of D(4)-pair {F_2k, 5F_2k}, Fibonacci Quart. 53 (2015), 124-129.

301. A. Srinivasan, D(-1)-quadruples and products of two primes, Glas. Mat. Ser. III 50 (2015), 261-268.

302. K. Meena, S. Vidhyalakshmi, M. A. Gopalan, R. Presenna, Special Dio-triples, JP J. Algebra Number Theory Appl. 31 (2014), 13-25.

303. Z. Zhang, The Diophantine equation (ax^k-1)(by^k-1) = abz^k-1, J. Number Theory 136 (2014), 252-260.

304. I. Soldo, Some Diophantine Problems over the Imaginary Quadratic Fields, Dissertation, University of Zagreb, 2012 (in Croatian).

305. Lj. Bacic, Sets in which xy + 4 is always a square and problem of the extensibility of some parametric Diophantine triples, Dissertation, University of Zagreb, 2014 (in Croatian).

306. M. Mikic, Mordell-Weil Groups and Isogenies of the Families of Elliptic Curves, Dissertation, University of Zagreb, 2014 (in Croatian).

307. K. Aktas, On the solutions of congruence equations in the Gaussian integers ring and biquadratic residues, Master Thesis, Selcuk University, 2008 (in Turkish).

308. L. Bapoungue, The system of Diophantine equations (u-1)x² - 4uy² = -12u-8 and (u+2)x² - 4uz² = -12u+8 , Sciencia Acta Xaveriana 4 (2013), 1-20.

309. M. Alp, N. Irmak, L. Szalay, Reduced diophantine quadruples with the binary recurrence G_n = AG_n-1-G_n-2, An. Stiint. Univ. "Ovidius" Constanta Ser. Mat. 23 (2015), 23-31.

310. N. Irmak, L. Szalay, Diophantine triples and reduced quadruples with the Lucas sequence of recurrence u_n = Au_n-1 - u_n-2, Glas. Mat. Ser. III 49 (2014), 303-312.

311. M. Alp, N. Irmak, L. Szalay, Balancing Diophantine triples with distance 1, Period. Math. Hungar. 71 (2015), 1-10.

312. M. Cipu, Further remarks on Diophantine quintuples, Acta Arith. 168 (2015), 201-219.

313. D. J. Platt, T. S. Trudgian, Diophantine quintuples containing triples of the first kind, Period. Math. Hungar. 72 (2016), 235-242.

314. T. S. Trudgian, Bounds on the number of Diophantine quintuples, J. Number Theory 157 (2015), 233-249.

315. A. Bérczes, F. Luca, I. Pink, V. Ziegler, Finiteness results for Diophantine triples with repdigit values, Acta Arith. 172 (2016), 133-148.

316. A. Filipin, A. Jurasic, On the size of Diophantine m-tuples for linear polynomials, Miskolc Math. Notes 17 (2016), 861-876.

317. M. Cipu, A. Filipin, Y. Fujita, Bounds for Diophantine quintuples II, Publ. Math. Debrecen 88 (2016), 59-78.

318. F. Izadi, F. Khoshnam, On elliptic curves via Heron triangles and Diophantine triples, J. Math. Ext. 8 (2014), 17-26.

319. Z. Cerin, G. M. Gianella, On Jones S(E)-triples and S(E)-quadruples in rings, Rend. Circ. Mat. Palermo (2) Suppl. No. 83 (2011), 95-109.

320. Z. Cerin, G. M. Gianella, Square in Euler triples from Pell and Pell-Lucas numbers, Rend. Circ. Mat. Palermo (2) Suppl. No. 84 (2012), 187-194.

321. C. A. Gomez Ruiz, F. Luca, Diophantine quadruples in the sequence of shifted Tribonacci numbers, Publ. Math. Debrecen 86 (2015), 473-491.

322. A. Bérczes, A. Dujella, L. Hajdu, Sz. Tengely, Finiteness results for F-Diophantine sets, Monatsh. Math. 180 (2016), 469-484.

323. A. Dujella, M. Kazalicki, M. Mikic, M. Szikszai, There are infinitely many rational Diophantine sextuples, Int. Math. Res. Not. IMRN 2017 (2) (2017), 490-508.

324. A. W. Dudek, On the number of divisors of n² - 1, Bull. Aust. Math. Soc. 93 (2016), 194-198.

325. M. Cipu, T. Trudgian, Searching for Diophantine quintuples, Acta Arith. 173 (2016), 365-382.

326. A. Bayad, A. Filipin, A. Togbé, Extension of a parametric family of Diophantine triples in Gaussian integers, Acta Math. Hungar. 148 (2016), 312-327.

327. C. Fuchs, C. Hutle, N. Irmak, F. Luca, L. Szalay, Only finitely many Tribonacci Diophantine triples exist, Math. Slovaca 67 (2017), 853-862.

328. Y. Fujita, T. Miyazaki, The regularity of Diophantine quadruples, Trans. Amer. Math. Soc. 370 (2018), 3803-3831.

329. K. Lapkova, Explicit upper bound for an average number of divisors of quadratic polynomials, Arch. Math. (Basel) 106 (2016), 247-256.

330. F. Bencherif, N. Benyahia Tani, S. Bouroubi, O. Kihel, Z. Yahi, Integer partitions into Diophantine pairs, Quaest. Math. 40 (2017), 435-442.

331. Bo He, A. Pinter, A. Togbé, S. Yang, Another generalization of a theorem of Baker and Davenport, J. Number Theory 182 (2018), 325-343.

332. Y. Zhang, G. Grossman, Diophantine triples and extendibility of {1,2,5} and {1,5,10}, Fibonacci Quart. 52 (2014), 212-215.

333. C. A. Gómez Ruiz, Números Tribonacci, S-unidades y triplas diofánticas, Rev. Integr. Temas Mat. 33 (2015), 121-133.

334. C. Fuchs, C. Hutle, F. Luca, L. Szalay, Diophantine triples and k-generalized Fibonacci sequences, Bull. Malays. Math. Sci. Soc. (2) 41 (2018), 1449-1465.

335. Y. Zhang, G. Grossman, On Diophantine triples and quadruples, Notes Number Theory Discrete Math. 21(4) (2015), 6-16.

336. A. Dujella, M. Jukic Bokun, I. Soldo, On the torsion group of elliptic curves induced by Diophantine triples over quadratic fields, Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Math. RACSAM 111 (2017), 1177-1185.

337. A. M. S. Ramasamy, Diophantine quadruples and near-diophantine quintuples from P_3,k sequences, Asian-Eur. J. Math. 10 (2017), 1750010 (13 pp)

338. M. Bliznac, A. Filipin, An upper bound for the number of Diophantine quintuples, Bull. Aust. Math. Soc. 94 (2016), 384-394.

339. A. Dujella, What is ... a Diophantine m-tuple?, Notices Amer. Math. Soc. 63 (2016), 772-774.

340. Lj. Bacic Djurackovic, A. Filipin, The extendibility of D(4)-pairs {F_2k, F_2k+6} and {P_2k, P_2k+4}, Rad Hrvat. Akad. Znan. Umjet. Mat. Znan. 20 (2016), 27-35.

341. A. Dujella and M. Kazalicki, More on Diophantine sextuples, in Number Theory - Diophantine problems, uniform distribution and applications, Festschrift in honour of Robert F. Tichy's 60th birthday (C. Elsholtz, P. Grabner, Eds.), Springer-Verlag, Berlin, 2017, pp. 227-235.

342. J. Harrington, L. Jones, A problem of Diophantus modulo a prime, Irish Math. Soc. Bull. 77 (2016), 45-49.

343. F. Luca, A. O. Munagi, Diophantine triples with values in the sequences of Fibonacci and Lucas numbers, Glas. Mat. Ser. III 52 (2017), 23-43.

344. A. Bayad, A. Dossavi-Yovo, A. Filipin, A. Togbé, On the extensibility of the D(4)-triple {k - 2, k + 2, 4k} over Gaussian integers, Notes Number Theory Discrete Math. 23 (2017), 1-26.

345. A. Dossavi-Yovo, Bo He, A. Togbé, The extensibility of the D(±k)-triple {k ∓ 1, k, 4k ∓ 1}, Afrika Mat. 28 (2017), 563-574.

346. B. He, F. Luca, A. Togbé, Diophantine triples of Fibonacci numbers, Acta Arith. 175 (2016) , 57-70.

347. A. Dujella, M. Kazalicki, Diophantine m-tuples in finite fields and modular forms, Res. Number Theory 7 (2021), Article number 3, (24pp)

348. P. E. Gibbs, Regular rational Diophantine sextuples, preprint.

349. P. E. Gibbs, A survey of rational Diophantine sextuples of low height, preprint.

350. B. He, A. Togbé, V. Ziegler, There is no Diophantine quintuple, Trans. Amer. Math. Soc. 371 (2019), 6665-6709.

351. N. Adžaga, A. Filipin, On the extension of D(-8k²)-pair {8k², 8k² + 1}, Mosc. Math. J. 17 (2017), 165-174.

352. D. M. Burton, Elementary Number Theory, 7th edition, McGraw-Hill, New York, 2011, p. 33.

353. T. Cai, The Book of Numbers, World Scientific, Singapore, 2017, pp. 206-209.

354. N. Irmak, M. Alp, Pellans sequence and its Diophantine triples, Publ. Inst. Math. 100 (2016), 259-269.

355. M. Cipu, Y. Fujita, M. Mignotte, Two-parameter families of uniquely extendable Diophantine triples, Sci. China Math. 61 (2018), 421-438.

356. S. Bujačić, A. Filipin, Linear forms in logarithms, in Diophantine Analysis: Course Notes from a Summer School (J. Steuding, Ed.), Birkhäuser, Basel, 2016, pp. 1-59.

357. I. Chajda, Diofantovské n-tice, Matematika - fyzika - informatika 26 (2017), 1-6.

358. Ö. Özer, On the some particular sets, Kirklareli University Journal of Engineering and Science 2 (2016) 99-108.

359. M. Bliznac Trebješanin, A. Filipin, A. Jurasić, On the polynomial quadruples with the property D(-1;1), Tokyo J. Math. 41 (2018), 527-540.

360. N. Adžaga, A. Dujella, D. Kreso, P. Tadić, Triples which are D(n)-sets for several n's, J. Number Theory 184 (2018), 330-341.

361. M. Bliznac Trebješanin, A. Filipin, Nonexistence of D(4)-quintuples, J. Number Theory 194 (2019), 170-217.

362. K. Lapkova, Explicit upper bound for the average number of divisors of irreducible quadratic polynomials, Monatsh. Math. 186 (2018), 663-673.

363. A. Filipin, The extension of some D(4)-pairs, Notes Number Theory Discrete Math. 23 (2017), 126-135.

364. A. Filipin, A. Jurasic, A polynomial variant of a problem of Diophantus and its consequences, Glas. Mat. Ser. III 54 (2019), 21-52.

365. F. Luca, Y. Fujita, On Diophantine quadruples of Fibonacci numbers, Glas. Mat. Ser. III 52 (2017), 221-234.

366. A. Dujella, M. Jukić Bokun, I. Soldo, A Pellian equation with primes and applications to D(-1)-quadruples, Bull. Malays. Math. Sci. Soc 42 (2019), 2915-2926.

367. J. B. Lee, J. Park, Some conditions on the form of third element from Diophantine pairs and its application, J. Korean Math. Soc. 55 (2018), 425-445.

368. M. Sadek, N. El Sissi, On large F-Diophantine sets, Monatsh. Math. 186 (2018), 703-710.

369. A. M. S. Ramasamy, Diophantine quadruples of numbers whose elements are in proportion, Tamkang J. Math. 48 (2017), 241-249.

370. M. Cipu, Y. Fujita, T. Miyazaki, On the number of extensions of a Diophantine triple, Int. J. Number Theory 14 (2018), 899-917.

371. K. Lapkova, On the average number of divisors of reducible quadratic polynomials, J. Number Theory 180 (2017), 710-729.

372. M. Stoll, Diagonal genus 5 curves, elliptic curves over Q(t), and rational diophantine quintuples, Acta Arith. 190 (2019), 239-261.

373. S. Cenberci, B. Peker, On some P₂ sets, Pure Mathematical Sciences 6 (2017), 61-66.

374. B. Peker, S. Cenberci, On the equations y² - 10x² = 9 and z² - 17x² = 16, International Mathematical Forum 12 (2017), 715-720.

375. G. Nyul, Diofantoszi számhalmazok, Középiskolai Matematikai és Fizikai Lapok 67 (2017), 391-395.

376. C. Fuchs, C. Hutle, F. Luca, Diophantine triples in linear recurrence sequences of Pisot type, Res. Number Theory 4 (2018), Paper No. 29, 22 pp.

377. M. Krizek, F. Luca, L. Somer, Aritmeticke vlastnosti Fibonacciovych cisel, Pokroky matematiky, fyziky a astronomie 50 (2005), 127-140.

378. A. Dujella, J. C. Peral, Elliptic curves induced by Diophantine triples, Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Math. RACSAM 113 (2019), 791-806.

379. G. K. Gözeri, On Pell, Pell-Lucas, and balancing numbers, J. Inequal. Appl. 2018 (2018), Paper No. 3, 16 pp.

380. M. Bliznac Trebješanin, Diophantine D(4)-m-tuples and Related Problems, Dissertation, University of Zagreb, 2018 (in Croatian).

381. A. Dujella, I. Gusic, V. Petricevic, P. Tadic, Strong Eulerian triples, Glas. Mat. Ser. III 53 (2018), 33-42.

382. Y. Bugeaud, Linear Forms in Logarithms and Applications, IRMA Lectures in Mathematics and Theoretical Physics Vol. 28, European Mathematical Society, 2018, Sections 3.8 and 5.4.

383. P. Gibbs, Diophantine quintuples over quadratic rings, preprint, 2018.

384. Y. Fujita, T. Miyazaki, Extendabilities of a Diophantine triple to quadruples, RIMS Kokyuroku 2014 (2017), 111-123. (in Japanese)

385. T. Trudgian, A wishlist for Diophantine quintuples, RIMS Kokyuroku 2014 (2017), 124-131.

386. M. Somanath, J. Kannan, K. Raja, Construction of a parametric family of Diophantine triples in integers, Indian Journal in Number Theory (2018), 1-6.

387. S. E. Rihane, M. O. Hernane, A. Togbé, On the D(4)-Diophantine triples of Fibonacci numbers, Fibonacci Quart. 56 (2018), 63-74.

388. N. Adzaga, A. Dujella, D. Kreso, P. Tadic, On Diophantine m-tuples and D(n)-sets, RIMS Kokyuroku 2092 (2018), 130-137.

389. B. He, K. Pu, R. Shen, A. Togbé, A note on the regularity of the Diophantine pair {k, 4k ± 4}, J. Theor. Nombres Bordeaux 30 (2018), 879-892.

390. M. Cipu, A. Filipin, Y. Fujita, An infinite two-parameter family of Diophantine triples, Bull. Malays. Math. Sci. Soc. 43 (2020), 481-498.

391. N. Adzaga, Diophantine m-tuples in the Rings of Integers, Dissertation, University of Zagreb, 2018 (in Croatian).

392. O. Cira, Diophantine triples of superior order, ISREIE Conference, 7th Edition, Mathematics & Computer Science (2018), 35-54.

393. Y. Fujita, F. Luca, There are no Diophantine quadruples of Fibonacci numbers, Acta Arith. 185 (2018), 19-38.

394. N. Adzaga, On the size of Diophantine m-tuples in imaginary quadratic number rings, Bull. Math. Sci. 11(1) (2021) 1950020 (10 pages).

395. V. Ziegler, On the existence of S-Diophantine quadruples, Glas. Mat. Ser. III 54 (2019), 279-319.

396. C. A. Gomez Ruiz, F. Luca, Diophantine quadruples with values in k-generalized Fibonacci numbers, Math. Slovaca 68 (2018), 939-949.

397. M. Cipu, A. Dujella, Y. Fujita, Diophantine triples with largest two elements in common, Period. Math. Hungar. 82 (2021), 56-68.

398. R. Becker, M. Ram Murty, Diophantine m-tuples with the property D(n), Glas. Mat. Ser. III 54 (2019), 65-75.

399. M. Cipu, A. Filipin, Y. Fujita, Diophantine pairs that induce certain Diophantine triples, J. Number Theory 210 (2020), 433-475.

400. J. Harrington, L. Jones, A modification of a problem of Diophantus, Math. Slovaca 68 (2018), 1343-1352.

401. M. Krizek, L. Somer, A. Solcova, Kouzlo cisel. Od velkych objevu k aplikacim, Academia, Praha, 2018, pp. 241-242.

402. K. Gueth, Diophantine triples in a Lucas-Lehmer sequence, Ann. Math. Inform. 49 (2018), 85-100.

403. A. Dujella, V. Petricevic, Diophantine quadruples with the properties D(n₁) and D(n₂), Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Math. RACSAM 114 (2020), Article 21 (9 pages).

404. M. Cipu, A new approach to the study of D(-1)-quadruples, RIMS Kokyuroku 2092 (2018), 122-129.

405. N. Mani, S. Rubinstein-Salzedo, Diophantine tuples over Z_p, Acta Arith. 197 (2021), 331-351.

406. A. Dujella, M. Kazalicki, V. Petricevic, Rational Diophantine sextuples with square denominators, J. Number Theory 205 (2019), 340-346.

407. T. Miyazaki, Coincidence between two binary recurrent sequences of polynomials arising from Diophantine triples, Tokyo J. Math. 42 (2019), 611-619.

408. M. Jukic Bokun, I. Soldo, On the extensibility of D(-1)-pairs containing Fermat primes, Acta Math. Hungar. 159 (2019), 89-108.

409. A. Dujella, M. Kazalicki, V. Petricevic, Rational Diophantine sextuples containing two regular quadruples and one regular quintuple, Acta Mathematica Spalatensia 1 (2021), 19-27.

410. A. E. Rihane, M. O. Hernane, A. Togbe, On Diophantine triples of Pell numbers, Colloq. Math. 156 (2019), 273-285.

411. A. Dujella, V. Petricevic, On the largest element in D(n)-quadruples, Indag. Math. (N.S.) 30 (2019) 1079-1086.

412. O. Ozer, Some results on especial Diophantine sets with size 3, Journal of Advanced Mathematics and Mathematics Educaton 2 (2019), 1-11.

413. Z. Franusic, B. Jadrijevic, D(n)-quadruples in the ring of integers of Q(√2,√3), Math. Slovaca 69 (2019), 1263-1278.

414. F. Luca, Diophantine S-quadruples with two primes which are twin, Acta Math. Hungar. 159 (2019), 589-602.

415. A. H. Phulpoto, I. Ahmed, A. Hameed, I. Soomro, R. Muhammed, I. A. Jokhio, R. chohan, A. N. Kalhoro, S. N. Phulpoto, A. D. Jumani, Diophantine Quadruple with D(9) property, IJCSNS International Journal of Computer Science and Network Security 19 (2019), 245-248.

416. J. Park, J. B. Lee, Some family of Diophantine pairs with Fibonacci numbers, Indian J. Pure Appl. Math. 19 (2019), 367-384.

417. N. Adzaga, A. Filipin, Z. Franusic, On the extensions of the Diophantine triples in Gaussian integers, Monatsh. Math. 197 (2022), 535-563.

418. A. N. Kalhoro, I. Soomro, A. H. Junejo, I. A. Memon, R. Muhammed, I. A. Jokhio, R. chohan, A. D. Jumani, Diophantine Quadruple with D(100) property, IJCSNS International Journal of Computer Science and Network Security 19 (2019), 236-238.

419. A. H. Phulpoto, I. Ahmed, I. Soomro, A. Hameed, R. Muhammed, I. A. Jokhio, R. Chohan, A. N. Kalhoro, S. N. Phulpoto, A. D. Jumani, Some polynomial formula of the Diophantine Quadruple with D(n) property, IJCSNS International Journal of Computer Science and Network Security 19 (2019), 249-251.

420. M. Bliznac Trebješanin, Extension of a Diophantine triple with the property D(4), Acta Math. Hungar. 163 (2021), 213-246.

421. S. Earp-Lynch, Diophantine Triples and Linear Forms in Logarithms, Master Thesis, Brock University, 2019.

422. B. Earp-Lynch, Linear Forms in Logarithms and Fibonacci Numbers, Master Thesis, Brock University, 2019.

423. Ö. Özer, Z. C. Sahin, On some particular regular Diophantine 3-tuples, Math. Nat. Sci. 3 (2018), 29-38.

424. A. M. Güloglu, M. Ram Murty, The Paley graph conjecture and Diophantine m-tuples, J. Combin. Theory Ser. A 170 (2020), Article 105155.

425. C. Fuchs, S. Heintze, Another S-unit variant of Diophantine tuples, Proc. Amer. Math. Soc. 149 (2021), 27-35.

426. A. Dujella, Number Theory, Skolska knjiga, Zagreb, 2019, (in Croatian), Sections 14.6, 16.7.

427. A. Dujella and J. C. Peral, Construction of high rank elliptic curves, J. Geom. Anal. 31 (2021), 6698-6724.

428. N. Adzaga, A. Filipin and Y. Fujita, The extension of the D(-k)-pair {k, k + 1} to a quadruple, Period. Math. Hungar. 85 (2022), 148-163.

429. A. Dujella, M. Paganin and M. Sadek, Strong rational Diophantine D(q)-triples, Indag. Math. (N.S.) 31 (2020), 505-511.

430. A. Dujella and V. Petricevic, Doubly regular Diophantine quadruples, Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Math. RACSAM 114 (2020), Article 189, (8pp)

431. S. Bouroubi and A. Debbache, Thue’s equation as a tool to solve two different problems, Acta Comment. Univ. Tartu. Math. 25 (2021), 153-156.

432. G. Drazic and M. Kazalicki, Rational D(q) quadruples, Indag. Math. (N.S.) 33 (2022), 440-449.

433. S. G. Rayaguru, G. K. Panda and A. Togbé, On Diophantine, pronic and triangular triples of balancing numbers, Math. Commun. 25 (2020), 137-155.

434. O. Aytekin Celik, Some P_s Diophantine triples for especial s integer, Journal of Advanced Mathematics and Mathematics Educaton 3 (2020), 1-9.

435. S. Gupta, D(-1) tuples in imaginary quadratic fields, Acta Math. Hungar. 164 (2021), 556-569.

436. A. M. S. Ramasamy, Polynomials yielding quadruples with property D(k), J. of Ramanujan Society of Mathematics and Mathematical Sciences 7 (2019), 53-64.

437. Y. Fujita, The number of irregular Diophantine quadruples for a fixed Diophantine pair or triple, Contemp. Math. 768 (2021), 105-118.

438. A. Dujella and J. C. Peral, High rank elliptic curves induced by rational Diophantine triples, Glas. Mat. Ser. III 55 (2020), 237-252.

439. A. Dujella and M. Mikic, Rank zero elliptic curves induced by rational Diophantine triples, Rad Hrvat. Akad. Znan. Umjet. Mat. Znan. 24 (2020), 29-37.

440. C. Fuchs, S. Heintze, A polynomial variant of Diophantine triples in linear recurrences, Period. Math. Hungar. 86 (2023), 289-299.

441. A. Chung, R. Raval, There is no Diophantine quintuple, Leicester Undergraduate Mathematical Journal 2 (2020).

442. A. Filipin, Z. Franusic, Diophantine Sets, Lecture notes, University of Zagreb, 2020 (in Croatian).

443. B. Earp-Lynch, S. Earp-Lynch, O. Kihel, On certain D(9) and D(64) Diophantine triples, Acta Math. Hungar. 162 (2020), 483-517.

444. J. Park, Relation between Diophantine triple and elliptic curve, J. Chungcheong Math. Soc. 33 (2020), 227-236.

445. A. Filipin, A. Jurasic, Diophantine quadruples in Z[i][X], Period. Math. Hungar. 82 (2021), 198-212.

446. J. Park, Integer points on the elliptic curves induced by Diophantine triples, Commun. Korean Math. Soc. 35 (2020), 745-757.

447. A. Dujella, Z. Franusic, V. Petricevic, Formulas for Diophantine quintuples containing two pairs of conjugates in some quadratic fields, Period. Math. Hungar. 85 (2022), 303-311.

448. J. Park, The extendibility of Diophantine pairs with property D(-1), Korean J. Math. 28 (2020), 539-554.

449. N. C. Bonciocat, M. Cipu, M. Mignotte, There is no Diophantine D(-1)-quadruple, J. London Math. Soc. 105 (2022), 63-99.

450. K. N. Adedji, A. Filipin, A. Togbé, The problem of the extension of D(4)-triple {1, b, c}, Rad Hrvat. Akad. Znan. Umjet. Mat. Znan. 26 (2022), 21-43.

451. V. Ziegler, Finding all S-Diophantine quadruples for a fixed set of primes S, Monatsh. Math. 196 (2021), 617-641.

452. A. Dujella, M. Kazalicki, V. Petricevic, D(n)-quintuples with square elements, Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Math. RACSAM 115 (2021), Article 172, (10pp)

453. A. Filipin, M. Jukic Bokun, I. Soldo, On D(-1)-triples {1, 4p² + 1, 1 - p} in the ring Z[√-p] with a prime p, Period. Math. Hungar. 85 (2022), 292-302.

454. N. Adzaga, A. Filipin, A. Jurasic, The extensibility of the Diophantine triple {2, b, c}, An. Stiint. Univ. "Ovidius" Constanta Ser. Mat. 29 (2021), 5-24.

455. M. Jukic Bokun, I. Soldo, Pellian equations of special type, Math. Slovaca 71 (2021), 1599-1607.

456. K. N. Adedji, A. Filipin, A. Togbé, On the family of Diophantine pairs {P_2k, 2P_2k+2}, Fibonacci Quart. 60 (2022), 25-39.

457. N. Irmak, Generalized Tribonacci Diophantine quadruples, Math. Rep. (Bucur.) 23 (2021), 465-474.

458. M. Kazalicki, B. Naskrecki (with an appendix by L. Lasic), Diophantine triples and K3 surfaces, J. Number Theory 236 (2022), 41-70.

459. S. Saranya, V. Pandichelvi, Classification of an exquisite diophantine 4-tuples bestow with an order, Malaya J. Mat. 9 (2021), 612-615.

460. S. Ibrahimpasic, Diophantine m-tuples, Master Thesis, University of Bihac, 2014 (in Bosnian).

461. B. Milosevic, Chord-Tangent Group Law on a Cubic Curves. Mordell’s Finite Generation Theorem, Master Thesis, University of Belgrade, 2020 (in Serbian).

462. A. Dujella, Number Theory, Skolska knjiga, Zagreb, 2021, Sections 14.6, 16.7.

463. K. N. Adedji, B. He, A. Pinter, A. Togbe, On the Diophantine pair {a, 3a}, J. Number Theory 227 (2021), 330-351.

464. A. E. Youmbai, M. Uludag, D. Behloul, Elliptic curve involving subfamilies of rank at least 5 over Q(t) or Q(t,k), Hacet. J. Math. Stat. 50 (2021), 721-731.

465. A. Dujella, G. Soydan, On elliptic curves induced by rational Diophantine quadruples, Proc. Japan Acad. Ser. A Math. Sci. 98 (2022), 1-6.

466. G. Drazic, Rational D(q)-quintuples, Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Math. RACSAM 116 (2022), Article 9, (18pp).

467. Z. Franusic, Diophantine quintuples containing two pairs of conjugates in some quadratic fields, Rad Hrvat. Akad. Znan. Umjet. Mat. Znan. 26 (2022), 45-53.

468. G. Drazic, A parametrization of rational D(q)-triples, Mat. Bilten 45 (2021), 7-16.

469. J. Park, Diophantine triple with Fibonacci numbers and elliptic curve, Commun. Korean Math. Soc. 36 (2021), 401-411.

470. J. Park, The extendibility of Diophantine pairs with Fibonacci numbers and some conditions, J. Chungcheong Math. Soc. 34 (2021), 209-219.

471. P. Gibbs, Diophantine quadruples and ideal solutions of the Prouhet-Tarry-Escott problem of size four, preprint, 2021.

472. B. Grechuk, Landscape of 21st Century Mathematics. Selected Advances, 2001–2020, Springer, Cham, 2021, Section 1.4, pp. 17-18.

473. G. Drazic, Rational D(q)-m-tuples, Dissertation, University of Zagreb, 2021 (in Croatian).

474. A. D. Denton, A holiday brain teaser, The Sunday Times, 4th August 1957, 18th August 1957.

475. M. Cipu, A. Dujella, Y. Fujita, Extensions of a Diophantine triple by adjoining smaller elements, Mediterr. J. Math. 19 (2022), Article 187, (20pp)

476. K. N. Adedji, A. Filipin, A. Togbé, The extension of the D(-k)-triple {1, k, k+1}, Acta Math. Hungar. 166 (2022), 407-422.

477. T. Hammonds, S. Kim, S. J. Miller, A. Nigam, K. Onghai, D. Saikia, L. M. Sharma, k-Diophantine m-tuples in finite fields, Int. J. Number Theory 19 (2023), 891-912.

478. A. B. Dixit, S. Kim, M. Ram Murty, Generalized Diophantine m-tuples, Proc. Amer. Math. Soc. 150 (2022), 1455-1465.

479. S. E. Rihane, F.Luca, A. Togbé, There are no Diophantine quadruples of Pell numbers, Int. J. Number Theory 18 (2022), 27-45.

480. Y. Fujita, I. Soldo, On D(-1)-tuples in the ring Z[√-k] with k > 0, Publ. Math. Debrecen 100 (2022), 49-67.

481. M. N. Deshpande, Diophantine triplets revisited, The Mathematical Gazette 90 (2006), 445-448.

482. C. Saranya, B. Achya, Diophantine triplets involving square pyramidal numbers, Advances and Applications in Mathematical Sciences 21 (2022), 1541-1547.

483. M. Bliznac Trebješanin, D(4)-triples with two largest elements in common, Math. Slovaca 73 (2023), 343-352.

484. M. Cipu, Y. Fujita, M. Mignotte, The unique extensions of two parametric families of Diophantine triples, RIMS Kokyuroku 2203 (2021), 41-47.

485. K. Chakraborty, S. Gupta, A. Hoque, Diophantine triples with the property D(n) for distinct n's, Mediterr. J. Math. 20 (2023), Article 31, (13pp)

486. M. Sadek, T. Yesin, Divisibility by 2 on quartic models of elliptic curves and rational Diophantine D(q)-quintuples, Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Math. RACSAM 116 (2022), Article 139.

487. A. Filipin, L. Szalay, Triangular Diophantine tuples from {1, 2}, Rad Hrvat. Akad. Znan. Umjet. Mat. Znan. 27 (2023), 55-70.

488. K. N. Adédji, M. Bliznac Trebješanin, A. Filipin, A. Togbé, On the D(4)-pairs {a,ka} with k ∈ {2,3,6}, Glas. Mat. Ser. III 58 (2023), 35-57.

489. M. N. Deshpande, Wonderland of Families of Diophantine triples, Second Edition, Nagpur, 2022.

490. K. Chakraborty, S. Gupta, A. Hoque, On a conjecture of Franusic and Jadrijevic: Counter-examples, Results Math. 78 (2023), Article 18.

491. A. Filipin, A. Jurasic, On the existence of D(-3)-quadruples over Z, Glas. Mat. Ser. III 57 (2022), 203-219.

492. M. Kazalicki, Quadratic twists of genus one curves and Diophantine quintuples, preprint, 2022.

493. S. Bhattacharjee, A. B. Dixit, D. Saikia, An effective bound on generalized Diophantine m-tuples, Bull. Aust. Math. Soc. 109 (2024), 242-253.

494. M. Le, A. Srinivasan, A note on Dujella's unicity conjecture, Glas. Mat. Ser. III 58 (2023), 59-65.

495. M. Bliznac Trebješanin, S. Bujačić, Polynomial D(4)-quadruples over Gaussian integers, Glas. Mat. Ser. III, to appear.

496. F. Luca, L. Szalay, Diophantine triples with distinct binary recurrences, Carpathian J. Math. 39 (2023), 255-264.

497. J. M. Mouanda, On Diophantine m-tuples over the set of commutative matrices, preprint, 2022.

498. J. M. Mouanda, On matrix Diophantine quadruples which cannot be extended to matrix Diophantine quintuples, preprint, 2022.

499. J. M. Mouanda, On matrix strong Diophantine 20-tuples, preprint, 2023.

500. I. E. Shparlinski, On the number of Diophantine m-tuples in finite fields, Finite Fields Appl. 90 (2023), Paper No. 102241

501. J. Park, Integer points on the elliptic curve with Fibonacci numbers, Indian J. Pure Appl. Math. 55 (2024), 480-488.

502. K. Chakraborty, S. Gupta, A. Hoque, Diophantine D(n)-quadruples in Z[√4k+2], Glas. Mat. Ser. III, to appear.

503. J. Kannan, M. Mahalakshmi, P. Nagajothi , Contriving of parametric sequences of Diophantine triples satisfying non-identical properties, in: Shodhgodavari: Advanced Knowledge from Multidisciplinary perspectives in Arts, Science, Humanities and Social Sciences, Multi Spectrum Publications, Kanyakumari, 2022.

504. J. Park, Complete solution of Diophantine pairs induced by some Fibonacci formula, Algebra Colloq. 30 (2023), 121-132.

505. N. Adzaga, G. Drazic, A. Dujella, A. Petho, Asymptotics of D(q)-pairs and triples via L-functions of Dirichlet characters, Ramanujan J., to appear.

506. M. Bliznac Trebješanin, P. Radic, On extensions of D(4)-triples by adjoining smaller elements, preprint, 2023.

507. M. Cipu, A. Dujella, Y. Fujita, Extensions of a Diophantine triple by adjoining smaller elements II, Period. Math. Hungar. 89 (2024), 54-60.

508. K. Santicola, Linear forms in logarithms, Summer project, University of Warwick, September 2022.

509. T. Cai, Perfect Numbers and Fibonacci Sequences, World Scientific, Singapore, 2022, Section 4.8, pp. 161-165.

510. Y. Fujita, I. Soldo, On the extendibility of certain D(−1)-pairs in imaginary quadratic rings, Indian J. Pure Appl. Math., to appear.

511. Y. Fujita, I. Soldo, The non-existence of D(−1)-quadruples extending certain pairs in imaginary quadratic rings, Acta Math. Hungar. 170 (2023), 455-482.

512. A. Dujella, High-rank elliptic curves with given torsion group and some applications, Number-Theoretic Methods in Cryptology (M. Grzeskowiak, J. Pieprzyk, J. Pomykala, ed.), Banach Center Publications 126, Institute of Mathematics, Polish Academy of Sciences, Warszawa, 2023, pp. 9-26.

513. S. Kim, C. H. Yip, S. Yoo, Diophantine tuples and multiplicative structure of shifted multiplicative subgroups, preprint, 2023.

514. M. Cipu, Y. Fujita, On the length of D(±1)-tuples in imaginary quadratic rings, Bull. Lond. Math. Soc. 56 (2024), 274-287.

515. K. Gyarmati, Elementary Methods to Combinatorial Number Theory, Lecture notes, Eötvös Loránd University, 2023, Chapter 4.

516. S. Gupta, Diophantine m-tuples in Quadratic Number Fields, PhD thesis, Harish-Chandra Research Institute, Prayagraj, 2023.

517. C. H. Yip, Multiplicatively reducible subsets of shifted perfect k-th powers and bipartite Diophantine tuples, preprint, 2023.

518. E. J. Barbeau, Power Play, The Mathematical Association of America, 1997, pp. 153-159.

519. Z. Franusic, A. Jurasic, On nonexistence of D(n)-quadruples, Math. Slovaca 74 (2024), 835-844.

520. A. Dujella, M. Kazalicki, V. Petricevic, Rational Diophantine sextuples with strong pair, preprint, 2024.

521. S. Kim, C. H. Yip, S. Yoo, Explicit constructions of Diophantine tuples over finite fields, Ramanujan J. 65 (2024), 163-172.

522. M. Cipu, Y. Fujita, M. Mignotte, Diophantine triples with three parameters, Res. Number Theory 10 (2024), Article number 44.

523. E. Barbeau, Gregarious and reclusive triples. Part A: A visit to the land of Fibonacci, Crux Mathematicorum 50 (2024), 190-192.

524. M. Jukic Bokun, I. Soldo, Extensions of D(−1)-pairs in some imaginary quadratic fields, New York J. Math. 30 (2024), 745-755.

525. N. Irmak, On k-generalized Fibonacci Diophantine triples, Math. Commun. 29 (2024), 203-216.

526. K. Brown, Numbers, 2023, Sections 1.7, 1.9, 1.12, 1.13, 3.2, 3.11, 14.5.

527. S. Kim, C. H. Yip, S. Yoo, Paley-like quasi-random graphs arising from polynomials, preprint, 2024.

528. C. H. Yip, S. Yoo, F-Diophantine sets over finite fields, preprint, 2024.

529. C. H. Yip, Improved upper bounds on Diophantine tuples with the property D(n), Bull. Aust. Math. Soc., to appear.

530. A. Dujella, Diophantine m-tuples and Elliptic Curves, Springer, Cham, 2024.

531. E. Barbeau, Gregarious and reclusive triples. Part B: A plethora of triples and quadruples, Crux Mathematicorum 50 (2024), 244-247.

532. C. H. Yip, Topics in arithmetic combinatorics, PhD Thesis, University of British Columbia, 2024.

533. E. Barbeau, Gregarious and reclusive triples. Part C: Finding triples when some elements are known, Crux Mathematicorum 50 (2024), 290-293.

534. R. Rathbun, 2001 Diophantine sextuples of low height, Zenodo, 2024, https://doi.org/10.5281/zenodo.13362704

535. T. Yesin Elsheikh, Divisibility of Rational Points on Elliptic Curves and Arithmetic Progressions in Polynomial Dynamical Systems, PhD thesis, Sabanci University, Istanbul, 2023.

536. R. Rathbun, The search for Diophantine sextuples and a possible septuple, distributed computing project, 2024, http://www.numbertheory.org/ntw/pdfs/search_for_Diophantine_sextuples.pdf

537. A. Dujella, Triples, quadruples and quintuples which are D(n)-sets for several n's, in: Class Groups of Number Fields and Related Topics (K. Chakraborty, A. Hoque and P. P. Pandey, Eds.), Springer, Cham, 2024, to appear.

538. G. McShane, Diophantine triples and Ptolemy relation, preprint, 2024.

539. N. Irmak, On k-generalized Fibonacci Diophantine triples, Math. Commun. 29 (2024), 203-216.

540. J. Badesa, On the asymptotics of D(n)-pairs and triples, preprint, 2024.

541. J. M. Mouanda, K. K. Vincent, On matrix strong Diophantine 27-tuples and matrix elliptic curves, Mathematics and Systems Science 2(2) (2024), Article ID: 2624.

542. G.Batta, L. Hajdu, A. Pongracz, On Diophantine graphs, preprint, 2024.

Classical references (Diophantus, Fermat, Euler)

Links to related sites

Papers of Andrej Dujella

1. Introduction
2. Diophantine quintuple conjecture
3. Sets with the property D(n)
4. Connections with Fibonacci numbers
5. Rational Diophantine m-tuples
6. Connections with elliptic curves
7. Various generalizations