There Are Infinitely Many Rational Diophantine Sextuples

A rational Diophantine m-tuple is a set of m non zero 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.

Andrej Dujella, Matija Kazalicki, Miljen Mikić, Márton Szikszai
Int Math Res Notices (2017) 2017 (2): 490-508. DOI: