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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 0<a<b<c 0 < a < b < c such that the product of any two of them is the value of a given polynomial with integer coefficients evaluated at an S S -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.

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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