# There are infinitely many rational Diophantine sextuples with square denominators

## TL;DR

This paper proves the existence of infinitely many rational Diophantine sextuples with all elements' denominators being perfect squares, extending the understanding of such sets in number theory.

## Contribution

It establishes the existence of infinitely many rational Diophantine sextuples with square denominators, a new property not previously demonstrated.

## Key findings

- Existence of infinitely many such sextuples proven.
- All elements in these sextuples have square denominators.
- Extends previous results on rational 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 in 2016 Dujella, Kazalicki, Miki\'c 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.