## Another $S$-unit variant of Diophantine tuples

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- by Clemens Fuchs and Sebastian Heintze
- Proc. Amer. Math. Soc.
**149**(2021), 27-35 - DOI: https://doi.org/10.1090/proc/15193
- Published electronically: October 16, 2020
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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.## References

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## Bibliographic Information

**Clemens Fuchs**- Affiliation: Department of Mathematics, University of Salzburg, Hellbrunnerstr. 34, A-5020 Salzburg, Austria
- MR Author ID: 705384
- ORCID: 0000-0002-0304-0775
- Email: clemens.fuchs@sbg.ac.at
**Sebastian Heintze**- Affiliation: Department of Mathematics, University of Salzburg, Hellbrunnerstr. 34, A-5020 Salzburg, Austria
- ORCID: 0000-0002-6356-1986
- Email: sebastian.heintze@sbg.ac.at
- Received by editor(s): October 21, 2019
- Received by editor(s) in revised form: April 20, 2020
- Published electronically: October 16, 2020
- Additional Notes: This research was supported by Austrian Science Fund (FWF): I4406.
- Communicated by: Rachel Pries
- © Copyright 2020 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**149**(2021), 27-35 - MSC (2010): Primary 11D61
- DOI: https://doi.org/10.1090/proc/15193
- MathSciNet review: 4172583