Diophantine quintuples containing triples of the first kind

Dave Platt; Tim Trudgian

Diophantine quintuples containing triples of the first kind

Number Theory 2015-02-27 v2

Authors: Dave Platt , Tim Trudgian

Abstract

We consider Diophantine quintuples $\{a, b, c, d, e\}$ , sets of distinct positive integers the product of any two elements of which is one less than a perfect square. Triples of the first kind are the subsets $\{a, b, d\}$ with $d> b^{5}$ . We show that there are no Diophantine quintuples containing triples of the first kind.

Keywords

diophantine quintuples diophantine triples perfect squares diophantine equations number theory positive integers

Cite

@article{arxiv.1501.04399,
  title  = {Diophantine quintuples containing triples of the first kind},
  author = {Dave Platt and Tim Trudgian},
  journal= {arXiv preprint arXiv:1501.04399},
  year   = {2015}
}

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10 pages

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