Bounds on the number of Diophantine quintuples

Tim Trudgian

Bounds on the number of Diophantine quintuples

Number Theory 2015-01-20 v1

Authors: Tim Trudgian

Abstract

We consider Diophantine quintuples $\{a, b, c, d, e\}$ . These are sets of distinct positive integers, the product of any two elements of which is one less than a perfect square. It is conjectured that there are no Diophantine quintuples; we improve on current estimates to show that there are at most $1.9\cdot 10^{29}$ Diophantine quintuples.

Keywords

diophantine quintuples upper bounds diophantine equations perfect squares number theory positive integers

Cite

@article{arxiv.1501.04401,
  title  = {Bounds on the number of Diophantine quintuples},
  author = {Tim Trudgian},
  journal= {arXiv preprint arXiv:1501.04401},
  year   = {2015}
}

Comments

16 pages

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