English

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)

R2 v1 2026-06-22T10:04:31.043Z