There are infinitely many rational Diophantine sextuples with square denominators

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 in 2016 Dujella, Kazalicki, Mikić and Szikszai proved that there are infinitely many of them. In this paper, we prove that there exist infinitely many rational Diophantine sextuples such that the denominators of all the elements in the sextuples are perfect squares.

6 pages

References in corpus (2)

• More on Diophantine sextuples
• Diagonal genus 5 curves, elliptic curves over $\mathbb{Q}(t)$, and rational diophantine quintuples

Cited by in corpus (7)

• Doubly regular Diophantine quadruples
• D(n)-quintuples with square elements
• Diophantine quadruples with the properties $D(n_1)$ and $D(n_2)$
• Strong rational Diophantine D(q)-triples
• High rank elliptic curves induced by rational Diophantine triples
• On elliptic curves induced by rational Diophantine quadruples
• On the largest element in D(n)-quadruples