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Mathematics > Number Theory

arXiv:1507.00569 (math)
[Submitted on 2 Jul 2015 (v1), last revised 30 Nov 2015 (this version, v3)]

Title:There are infinitely many rational Diophantine sextuples

Authors:Andrej Dujella, Matija Kazalicki, Miljen Mikić, Márton Szikszai
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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. In this paper, we prove that there exist infinitely many rational Diophantine sextuples.
Comments: 15 pages; a minor revision (one section added)
Subjects: Number Theory (math.NT)
Cite as: arXiv:1507.00569 [math.NT]
  (or arXiv:1507.00569v3 [math.NT] for this version)
  https://doi.org/10.48550/arXiv.1507.00569
Journal reference: Int. Math. Res. Not. IMRN 2017 (2) (2017), 490-508
Related DOI: https://doi.org/10.1093/imrn/rnv376

Submission history

From: Matija Kazalicki [view email]
[v1] Thu, 2 Jul 2015 13:14:47 UTC (13 KB)
[v2] Thu, 16 Jul 2015 21:18:31 UTC (13 KB)
[v3] Mon, 30 Nov 2015 14:23:18 UTC (15 KB)
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