There are infinitely many rational Diophantine sextuples

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.

15 pages; a minor revision (one section added)

References in corpus (1)

• A database of number fields

Cited by in corpus (15)

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• D(n)-quintuples with square elements
• Diophantine quadruples with the properties $D(n_1)$ and $D(n_2)$
• Rational $D(q)$-quadruples
• Strong Eulerian triples
• High rank elliptic curves induced by rational Diophantine triples
• Strong rational Diophantine D(q)-triples
• On the torsion group of elliptic curves induced by Diophantine triples over quadratic fields
• On elliptic curves induced by rational Diophantine quadruples
• On the largest element in D(n)-quadruples
• Rational $D(q)$-quintuples