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Searching for Diophantine quintuples

Mihai CipuTim Trudgian — 2016

Acta Arithmetica

We consider Diophantine quintuples a, b, c, d, e. These are sets of 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 5 . 441 · 10 26 Diophantine quintuples.

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