More on Diophantine sextuples

Abstract

A rational Diophantine m-tuple is a set of m nonzero rationals such that the product of any two of them increased by 1 is a perfect square. The first rational Diophantine quadruple was found by Diophantus, while Euler proved that there are infinitely many rational Diophantine quintuples. In 1999, Gibbs found the first example of a rational Diophantine sextuple, and Dujella, Kazalicki, Mikic and Szikszai recently proved that there exist infinitely many rational Diophantine sextuples. In this paper, generalizing the work of Piezas, we describe a method for generating new parametric formulas for rational Diophantine sextuples.

to appear 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

Cited by in corpus (10)

• There are infinitely many rational Diophantine sextuples with square denominators
• Diophantine m-tuples in finite fields and modular forms
• Doubly regular Diophantine quadruples
• D(n)-quintuples with square elements
• Diophantine quadruples with the properties $D(n_1)$ and $D(n_2)$
• Rational $D(q)$-quadruples
• Strong Eulerian triples
• High rank elliptic curves induced by rational Diophantine triples
• On elliptic curves induced by rational Diophantine quadruples
• Rational $D(q)$-quintuples