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arXiv · 2610.00893

Powers in orbits and semigroups generated by polynomials

Alina Ostafe·Dat T. Tran
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Abstract

In this paper, we study the presence of perfect powers in orbits of polynomials, or of semigroups generated by a finite family of polynomials, defined over a number field. In particular, we correct and generalize a result of Ahmadi et al. (2012), showing that multiplicative shifts of perfect powers in orbits can be detected by a finite algorithm. We also give a finiteness result on elements in orbits satisfying certain multiplicative relations.

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Alina Ostafe, Dat T. Tran. 2026-10-01. Powers in orbits and semigroups generated by polynomials. https://arxiv.org/abs/2610.00893

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