Publications of Andrej Dujella

(with papers in pdf format)


  1. A. Dujella and L. Szalay, Four squares from three numbers, preprint. (4pp)

  2. A. Dujella, J. Jaksetic and J. Pecaric, Fibonacci power means, Fibonacci Quart., to appear. (7pp)

  3. A. Dujella, J. Jaksetic and J. Pecaric, Fibonacci numbers and Hölder inequality, Bull. Transilv. Univ. Brasov Ser. III, to appear. (10pp)

  4. A. Dujella, M. Kazalicki and V. Petricevic, Rational Diophantine sextuples with strong pair, Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Math. RACSAM 119 (2025), Article 36, (10pp)

  5. N. Adzaga, G. Drazic, A. Dujella and A. Petho, Asymptotics of D(q)-pairs and triples via L-functions of Dirichlet characters, Ramanujan J. 66 (2025), Article 11, (23pp)

  6. A. Dujella, Triples, quadruples and quintuples which are D(n)-sets for several n's, in: Class Groups of Number Fields and Related Topics. ICCGNERT 2021, ICCGNERT 2022 (K. Chakraborty, A. Hoque and P. P. Pandey, Eds.), Springer, Singapore, 2024, pp. 77-92.

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

  8. A. Dujella and J. C. Peral, An elliptic curve over Q(u) with torsion Z/4Z and rank 6, Rad Hrvat. Akad. Znan. Umjet. Mat. Znan. 28 (2024), 185-192.

  9. 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.

  10. A. Dujella, K. Gyory, P. Michaud-Jacobs and A. Pinter, On power values of pyramidal numbers, II, Acta Arith. 208 (2023), 199-213.

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

  12. Y. Bugeaud, A. Dujella, W. Fang, T. Pejkovic and B. Salvy, Absolute root separation, Experiment. Math. 31 (2022), 806-813.

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

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

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

  16. A. Dujella, M. Kazalicki and J. C. Peral, Elliptic curves with torsion groups Z/8Z and Z/2Z × Z/6Z, Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Math. RACSAM 115 (2021), Article 169, (24pp)

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

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

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

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

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

  22. 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.

  23. 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)

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

  25. A. Dujella and 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, (9pp)

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

  27. A. Dujella and F. Luca, On fundamental units of real quadratic fields of class number 1, Arch. Math. (Basel) 113 (2019), 349-353.

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

  29. A. Bérczes, A. Dujella, L. Hajdu, N. Saradha and R. Tijdeman, Products of factorials which are powers, Acta Arith. 190 (2019), 339-350.

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

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

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

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

  34. N. Adzaga, A. Dujella, D. Kreso and P. Tadic, Triples which are D(n)-sets for several n's, J. Number Theory 184 (2018), 330-341.

  35. Y. Bugeaud, A. Dujella, T. Pejkovic and B. Salvy, Absolute real root separation, Amer. Math. Monthly 124 (2017), 930-936.

  36. A. Dujella and T. Pejkovic, Root separation for reducible monic polynomials of odd degree, Rad Hrvat. Akad. Znan. Umjet. Mat. Znan. 21 (2017), 21-27.

  37. A. Dujella, M. Jukic Bokun and 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.

  38. 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.

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

  40. A. Dujella, J. C. Peral and P. Tadic, Elliptic curves with torsion group Z/6Z, Glas. Mat. Ser. III 51 (2016), 321-333.

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

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

  43. A. Dujella, I. Gusic and P. Tadic, The rank and generators of Kihara's elliptic curve with torsion Z/4Z over Q(t), Proc. Japan Acad. Ser. A Math. Sci. 91 (2015), 105-109.

  44. A. Dujella and J. C. Peral, Elliptic curves with torsion group Z/8Z or Z/2Z × Z/6Z, in Trends in Number Theory, Contemp. Math. 649 (2015), 47-62.

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

  46. A. S. Janfada, S. Salami, A. Dujella and J. C. Peral, On the high rank π/3 and 2π/3 - congruent number elliptic curves, Rocky Mountain J. Math. 44 (2014), 1867-1880.

  47. A. Dujella and J. C. Peral, Elliptic curves coming from Heron triangles, Rocky Mountain J. Math. 44 (2014), 1145-1160.

  48. A. Dujella, I. Gusic and L. Lasic, On quadratic twists of elliptic curves y2 = x(x - 1)(x - λ), Rad Hrvat. Akad. Znan. Umjet. Mat. Znan. 18 (2014), 27-34.

  49. A. Dujella, F. Najman, N. Saradha and T. N. Shorey, Products of three factorials, Publ. Math. Debrecen 85 (2014), 123-130.

  50. J. Aguirre, A. Dujella, M. Jukic Bokun and J. C. Peral, High rank elliptic curves with prescribed torsion group over quadratic fields, Period. Math. Hungar. 68 (2014), 222-230.

  51. 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.

  52. J. Bosman, P. Bruin, A. Dujella and F. Najman, Ranks of elliptic curves with prescribed torsion over number fields, Int. Math. Res. Not. IMRN 2014 (11) (2014), 2885-2923.

  53. A. Dujella and 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.

  54. Y. Bugeaud and A. Dujella, Root separation for reducible integer polynomials, Acta Arith. 162 (2014), 393-403.

  55. A. Bérczes, A. Dujella and L. Hajdu, Some Diophantine properties of the sequence of S-units, J. Number Theory 138 (2014), 48-68.

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

  57. J. Aguirre, A. Dujella and J. C. Peral, Arithmetic progressions and Pellian equations, Publ. Math. Debrecen 83 (2013), 683-695.

  58. A. Dujella and C. Elsholtz, Sumsets being squares, Acta Math. Hungar. 141 (2013), 353-357.

  59. A. Dujella and J. C. Peral, Elliptic curves and triangles with three rational medians, J. Number Theory 133 (2013), 2083-2091.

  60. A. Dujella and F. Luca, On a variation of a congruence of Subbarao, J. Aust. Math. Soc. 93 (2012), 85-90.

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

  62. A. Dujella and F. Najman, Elliptic curves with large torsion and positive rank over number fields of small degree and ECM factorization, Period. Math. Hungar. 65 (2012), 193-203.

  63. S. Diaz Alvarado, A. Dujella and F. Luca, On a conjecture regarding balancing with powers of Fibonacci numbers, Integers 12A (2012), #A2. (29pp)

  64. A. Dujella, K. Gyory and A. Pinter, On power values of pyramidal numbers, I, Acta Arith. 155 (2012), 217-226.

  65. A. Dujella and F. Luca, On the sum of two divisors of (n2 + 1)/2, Period. Math. Hungar. 65 (2012), 83-96.

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

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

  68. 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.

  69. A. Dujella and T. Pejkovic, Root separation for reducible monic quartics, Rend. Semin. Mat. Univ. Padova 126 (2011), 63-72.

  70. Y. Bugeaud and A. Dujella, Root separation for irreducible integer polynomials, Bull. Lond. Math. Soc. 43 (2011), 1239-1244.

  71. A. Dujella, B. Ibrahimpasic and B. Jadrijevic, Solving a family of quartic Thue inequalities using continued fractions, Rocky Mountain J. Math. 41 (2011), 1173-1182.

  72. A. Dujella, On Hall's conjecture, Acta Arith. 147 (2011), 397-402.

  73. 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.

  74. A. Dujella and M. Jukic Bokun, On the rank of elliptic curves over Q(i) with torsion group Z/4Z × Z/4Z, Proc. Japan Acad. Ser. A Math. Sci. 86 (2010), 93-96.

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

  76. A. Dujella, A. S. Janfada and S. Salami, A search for high rank congruent number elliptic curves, J. Integer Seq. 12 (2009), Article 09.5.8 (11pp)

  77. A. Dujella, A variant of Wiener's attack on RSA, Computing 85 (2009), 77-83.

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

  79. A. Dujella and B. Ibrahimpasic, On Worley's theorem in Diophantine approximations, Ann. Math. Inform. 35 (2008), 61-73.

  80. A. Dujella, A. Petho and P. Tadic, On arithmetic progressions on Pellian equations, Acta Math. Hungar. 120 (2008), 29-38.

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

  82. 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.

  83. 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.

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

  85. A. Dujella and I. Gusic, Decomposition of a recursive family of polynomials, Monatsh. Math. 152 (2007), 97-104.

  86. Y. Bugeaud, A. Dujella and M. Mignotte, On the family of Diophantine triples {k - 1, k + 1, 16k3 - 4k}, Glasgow Math. J. 49 (2007), 333-344.

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

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

  89. A. Dujella and Z. Franusic, On differences of two squares in some quadratic fields, Rocky Mountain J. Math. 37 (2007), 429-453.

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

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

  92. A. Dujella and I. Gusic, Indecomposability of polynomials and related Diophantine equations, Q. J. Math. (Oxford) 57 (2006), 193-201.

  93. A. Dujella, I. Gusic and R. F. Tichy, On the indecomposability of polynomials, Österreich. Akad. Wiss. Math.-Natur. Kl. Sitzungsber. II 214 (2005), 81-88.

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

  95. 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.

  96. A. Dujella and V. Petricevic, Square roots with many good approximants, Integers 5(3) (2005), #A6. (13pp)

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

  98. A. Dujella, Continued fractions and RSA with small secret exponent, Tatra Mt. Math. Publ. 29 (2004), 101-112.

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

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

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

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

  103. A. Dujella and B. Jadrijevic, A family of quartic Thue inequalities, Acta Arith. 111 (2004), 61-76.

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

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

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

  107. A. Dujella, An example of elliptic curve over Q with rank equal to 15, Proc. Japan Acad. Ser. A Math. Sci. 78 (2002), 109-111.

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

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

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

  111. A. Dujella and B. Jadrijevic, A parametric family of quartic Thue equations, Acta Arith. 101 (2002), 159-170.

  112. A. Dujella and R. F. Tichy, Diophantine equations for second order recursive sequences of polynomials, Quart. J. Math. Oxford Ser. (2) 52 (2001), 161-169.

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

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

  115. A. Dujella, Newton's formula and continued fraction expansion of sqrt(d), Experiment. Math. 10 (2001), 125-131.

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

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

  118. A. Dujella, A parametric family of elliptic curves, Acta Arith. 94 (2000), 87-101; extended version. (41pp)

  119. 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.

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

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

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

  123. A. Dujella, A bijective proof of Riordan's theorem on powers of Fibonacci numbers, Discrete Math. 199 (1999), 217-220.

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

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

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

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

  128. 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.

  129. 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.

  130. 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.

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

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

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

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

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

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

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

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

Book Number Theory

Book Diophantine m-tuples and Elliptic Curves

Publications in Croatian

Lectures on conferences

Invited lectures

Diophantine m-tuples page

Andrej Dujella home page