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arXiv · 1507.00569

There are infinitely many rational Diophantine sextuples

Andrej Dujella·Matija Kazalicki·Miljen Mikić·Márton Szikszai
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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. In this paper, we prove that there exist infinitely many rational Diophantine sextuples.

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Andrej Dujella, Matija Kazalicki, Miljen Mikić, Márton Szikszai. 2015-11-30. There are infinitely many rational Diophantine sextuples. https://doi.org/10.1093/imrn%2Frnv376

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