Searching for Diophantine quintuples

Date

2016-05-18

Authors

Cipu, Mihai
Trudgian, Tim

Journal Title

Journal ISSN

Volume Title

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.

Description

Keywords

Diophantine m-tuples, Pell equations, linear forms in logarithms

Citation

Source

Acta Arithmetica

Type

Journal article

Book Title

Entity type

Access Statement

Open Access

License Rights

Restricted until