Another 𝑆-unit variant of Diophantine tuples

Fuchs, Clemens; Heintze, Sebastian

doi:10.1090/proc/15193

Another $S$-unit variant of Diophantine tuples
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by Clemens Fuchs and Sebastian Heintze PDF

Proc. Amer. Math. Soc. 149 (2021), 27-35 Request permission

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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