Searching for Diophantine quintuples

Mihai Cipu, Tim Trudgian

Published 2015-08-10Version 1

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 $1.18\cdot 10^{27}$ Diophantine quintuples.