More on Diophantine sextuples
Andrej Dujella, Matija Kazalicki
TL;DR
This paper develops a method to generate new parametric formulas for rational Diophantine sextuples, extending previous work and contributing to the understanding of these special sets of rational numbers.
Contribution
It introduces a generalized approach for creating parametric formulas for rational Diophantine sextuples, building on prior research.
Findings
New parametric formulas for rational Diophantine sextuples
Extension of previous methods for generating sextuples
Potential for discovering infinitely many 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, and Dujella, Kazalicki, Mikic and Szikszai recently proved that there exist infinitely many rational Diophantine sextuples. In this paper, generalizing the work of Piezas, we describe a method for generating new parametric formulas for rational Diophantine sextuples.
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