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Published in:
2017 | OriginalPaper | Chapter
More on Diophantine Sextuples
Authors : Andrej Dujella, Matija Kazalicki
Published in: Number Theory – Diophantine Problems, Uniform Distribution and Applications
Publisher: Springer International Publishing
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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, Mikić 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.