Preface
Page v, line 20: The current number of references on the web page [121] https://web.math.pmf.unizg.hr/~duje/dtuples.html is 543.
2.5 Rank of Elliptic Curves
Page 55: The current recond for the rank of elliptic curves over Q is the curve with rank ≥ 29 found by N. Elkies and Z. Klagsbrun in August 2024:
y2 + xy = x3 - 27006183241630922218434652145297453784768054621836357954737385x
+ 55258058551342376475736699591118191821521067032535079608372404779149413277716173425636721497.
Table 2.1 on p.56 and Table 2.2 on p.71 should be updated accordingly.
Page 73: In Table 2.4, in rows corresponding to Z/7Z and Z/9Z, it should be added "Youmbai (2024)".
3.11 Exercises
Concering Exercise 12 on page 166, let us mention that in the recent paper:
A. Dujella, M. Kazalicki, V. Petričević, Rational Diophantine sextuples with strong pair,
preprint, 2024,
it is shown that there exist infinitely many rational Diophantine sextuples
{a,b,c,d,e,f} with the property that
a2+1 and b2+1 are perfect squares.
5.1 Existence of D(n)-quadruples
Page 282, line 2: } is missing after 20. (Thanks to Mihai Cipu.)
5.2 Bounds for the Size of D(n)-tuples
Page 294, Remark 5.2.13: In the recent paper
C. H. Yip, Improved upper bounds on Diophantine tuples with the property D(n),
Bull. Aust. Math. Soc., to appear,
it is shown that Bn = O(log log |n|) and
Mn ≤ (2+o(1)) log |n|.
References
In reference [143], instead of "Preprint (2023). arXiv: 2304.01775" it should be "Ramanujan J., to appear.".
You may send your comments, remarks and suggestions on the book by e-mail to duje@math.hr. I will be grateful to anyone who points out inaccuracies or errors in the book.
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