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arXiv · 1903.02805

There are infinitely many rational Diophantine sextuples with square denominators

Andrej Dujella·Matija Kazalicki·Vinko Petričević
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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.

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Andrej Dujella, Matija Kazalicki, Vinko Petričević. 2019-03-07. There are infinitely many rational Diophantine sextuples with square denominators. https://doi.org/10.1016/j.jnt.2019.06.006

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