There are infinitely many rational Diophantine sextuples
Number Theory
2017-03-08 v3
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.
Keywords
Cite
@article{arxiv.1507.00569,
title = {There are infinitely many rational Diophantine sextuples},
author = {Andrej Dujella and Matija Kazalicki and Miljen Mikić and Márton Szikszai},
journal= {arXiv preprint arXiv:1507.00569},
year = {2017}
}
Comments
15 pages; a minor revision (one section added)