Bounds on the number of Diophantine quintuples

Date

2015

Authors

Trudgian, Timothy

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Publisher

Academic Press

Abstract

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.

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Citation

Source

Journal of Number Theory

Type

Journal article

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DOI

10.1016/j.jnt.2015.05.004

Restricted until

2037-12-31