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Bounds on the number of Diophantine quintuples

Trudgian, Timothy


We consider Diophantine quintuples {a,b,c,d,e}{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 2.3⋅10292.3⋅1029 Diophantine quintuples.

CollectionsANU Research Publications
Date published: 2015
Type: Journal article
Source: Journal of Number Theory
DOI: 10.1016/j.jnt.2015.05.004


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