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arXiv · 1910.09285

Yet another $S$-unit variant of Diophantine tuples

Clemens Fuchs·Sebastian Heintze
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Abstract

We show that there are only finitely many triples of integers $ 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 $-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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Clemens Fuchs, Sebastian Heintze. 2019-10-21. Yet another $S$-unit variant of Diophantine tuples. https://doi.org/10.1090/proc/15193

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