On Diophantine triples and quadruples

Yifan Zhang and G. Grossman
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 21, 2015, Number 4, Pages 6—16
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Authors and affiliations

Yifan Zhang
Department of Mathematics, Central Michigan University
Mount Pleasant, MI, USA

G. Grossman
Department of of Mathematics, Central Michigan University
Mount Pleasant, MI, USA


In this paper we consider Diophantine triples {a, b, c} (denoted D(n)-3-tuples) and give necessary and sufficient conditions for existence of integer n given the 3-tuple {a, b, c} so that ab + n, ac + n, bc + n are all squares of integers. Several examples as applications of the main results, related to both Diophantine triples and quadruples, are given.


  • Diophantine triples and quadruples
  • Necessary and sufficient conditions

AMS Classification

  • 11D99


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Cite this paper

Zhang, I. & Grossman, G. (2015). On Diophantine triples and quadruples, 21(4), 6-16.

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