Diophantine quintuples containing triples of the first kind
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> b5. We show that there are no Diophantine quintuples containing triples of the first kind.
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