There are infinitely many rational Diophantine sextuples
Andrej Dujella, Matija Kazalicki, Miljen Miki\'c, M\'arton Szikszai
TL;DR
This paper proves that there are infinitely many rational Diophantine sextuples, extending the known examples and demonstrating an infinite family of such sets with special multiplicative properties.
Contribution
The paper establishes the existence of infinitely many rational Diophantine sextuples, a significant advancement beyond previous isolated examples.
Findings
Existence of infinitely many rational Diophantine sextuples
Construction method for such sextuples
Extension of known finite examples to infinite families
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.
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