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On Diophantine quintuple conjecture

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Publication:464688
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DOI10.3792/pjaa.90.84zbMath1307.11039arXiv1401.5195OpenAlexW1988399986WikidataQ123144176 ScholiaQ123144176MaRDI QIDQ464688

Bo He, Wenquan Wu

Publication date: 29 October 2014

Published in: Proceedings of the Japan Academy. Series A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1401.5195


zbMATH Keywords

Pell equationsDiophantine equationsDiophatine \(m\)-tuples


Mathematics Subject Classification ID

Quadratic and bilinear Diophantine equations (11D09) Counting solutions of Diophantine equations (11D45)


Related Items

Searching for Diophantine quintuples ⋮ Diophantine quadruples and near-Diophantine quintuples from P3,K sequences ⋮ There is no Diophantine quintuple ⋮ Bounds on the number of Diophantine quintuples ⋮ Further remarks on Diophantine quintuples



Cites Work

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  • On Diophantine quintuples and \(D(-1)\)-quadruples
  • An absolute bound for the size of Diophantine \(m\)-tuples
  • The extensibility of Diophantine pairs \(\{k - 1,k+1\}\)
  • An explicit lower bound for a homogeneous rational linear form in the logarithms of algebraic numbers. II
  • The number of Diophantine quintuples
  • There are only finitely many Diophantine quintuples
  • The number of Diophantine quintuples II
  • THE EQUATIONS 3x2−2 = y2 AND 8x2−7 = z2
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