Elsevier

Indagationes Mathematicae

Volume 25, Issue 1, 5 January 2014, Pages 131-136
Indagationes Mathematicae

Diophantine m-tuples with elements in arithmetic progressions

https://doi.org/10.1016/j.indag.2013.08.006Get rights and content
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Abstract

In this paper, we consider the problem of existence of Diophantine m-tuples which are (not necessarily consecutive) elements of an arithmetic progression. We show that for n3 there does not exist a Diophantine quintuple {a,b,c,d,e} such that abcde(modn). On the other hand, for any positive integer n there exist infinitely many Diophantine triples {a,b,c} such that abc0(modn).

Keywords

Diophantine m-tuples
Arithmetic progressions
Pellian equations

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