Diophantine quintuples containing triples of the first kind

Dave Platt; Tim Trudgian

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arXiv · 1501.04399

Diophantine quintuples containing triples of the first kind

Dave Platt·Tim Trudgian

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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.

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Dave Platt, Tim Trudgian. 2015-02-26. Diophantine quintuples containing triples of the first kind. https://arxiv.org/abs/1501.04399

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