Andrej Dujella: Diophantine m-tuples and Elliptic Curves - Errata et addenda

List of corrections and additional comments to the book Diophantine m-tuples and Elliptic Curves, Springer, 2024

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 531.

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), preprint, 2024,
it is shown that B_n = O(log log |n|) and M_n ≤ (2+o(1)) log |n|.

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.