Bounds on the number of Diophantine quintuples

Tim Trudgian

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arXiv · 1501.04401

Bounds on the number of Diophantine quintuples

Tim Trudgian

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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.

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Tim Trudgian. 2015-01-19. Bounds on the number of Diophantine quintuples. https://arxiv.org/abs/1501.04401

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