Yet another $S$-unit variant of Diophantine tuples
Number Theory
2023-04-12 v1
Abstract
We show that there are only finitely many triples of integers such that the product of any two of them is the value of a given polynomial with integer coefficients evaluated at an -unit that is also a positive integer. The proof is based on a result of Corvaja and Zannier and thus is ultimately a consequence of the Schmidt subspace theorem.
Cite
@article{arxiv.1910.09285,
title = {Yet another $S$-unit variant of Diophantine tuples},
author = {Clemens Fuchs and Sebastian Heintze},
journal= {arXiv preprint arXiv:1910.09285},
year = {2023}
}
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9 pages