More on Diophantine Sextuples

Andrej Dujella () and Matija Kazalicki ()
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Andrej Dujella: University of Zagreb, Department of Mathematics
Matija Kazalicki: University of Zagreb, Department of Mathematics

A chapter in Number Theory – Diophantine Problems, Uniform Distribution and Applications, 2017, pp 227-235 from Springer

Abstract: 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.

Keywords: 11D09; 11G05; 11Y50 (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-55357-3_11

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DOI: 10.1007/978-3-319-55357-3_11

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