Bounds on the number of Diophantine quintuples
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· 1029 Diophantine quintuples.
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