There are infinitely many rational Diophantine sextuples

By Andrej Dujella, Matija Kazalicki, Miljen Miki'c, Márton Szikszai. 2015

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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.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/607f6901c5c98a58dc71dfa66c3a4f8321812bab