Bounds on the number of Diophantine quintuples
arXiv:1501.04401
Abstract
We consider Diophantine quintuples . 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 Diophantine quintuples.
16 pages