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arXiv · 1609.06986

More on Diophantine sextuples

Andrej Dujella·Matija Kazalicki
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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 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.

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Andrej Dujella, Matija Kazalicki. 2016-09-22. More on Diophantine sextuples. https://doi.org/10.1007/978-3-319-55357-3_11

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