Searching for Diophantine quintuples

Cipu, Mihai; Trudgian, Tim

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Searching for Diophantine quintuples

Date

2016-05-18

Authors

Cipu, Mihai

Trudgian, Tim

Publisher

Polish Academy of Sciences, Institute of Mathematics

Abstract

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⋅10²⁶ Diophantine quintuples.