Bounds on the number of Diophantine quintuples

Tim Trudgian

doi:10.1016/j.jnt.2015.05.004

Bounds on the number of Diophantine quintuples

Tim Trudgian^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

18 Citations (Scopus)

Abstract

We consider Diophantine quintuples {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{dot operator}10²⁹ Diophantine quintuples.

Original language	English
Pages (from-to)	233-249
Number of pages	17
Journal	Journal of Number Theory
Volume	157
DOIs	https://doi.org/10.1016/j.jnt.2015.05.004
Publication status	Published - 1 Dec 2015

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title = "Bounds on the number of Diophantine quintuples",

abstract = "We consider Diophantine quintuples {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{dot operator}1029 Diophantine quintuples.",

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N2 - We consider Diophantine quintuples {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{dot operator}1029 Diophantine quintuples.

AB - We consider Diophantine quintuples {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{dot operator}1029 Diophantine quintuples.

KW - Diophantine equations

KW - Diophantine quintuples

KW - Linear independence of logarithms

KW - Pell equations

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JO - Journal of Number Theory

JF - Journal of Number Theory

ER -

Bounds on the number of Diophantine quintuples

Abstract

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