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PreprintarXiv licencearXiv

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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Cite

BibTeXRIS
BibTeX
@misc{ostafe2026powers,
  title = {{Powers in orbits and semigroups generated by polynomials}},
  author = {Alina Ostafe and Dat T. Tran},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.00893},
  eprint = {2610.00893},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.00893},
}
RIS
TY  - UNPB
TI  - Powers in orbits and semigroups generated by polynomials
AU  - Alina Ostafe
AU  - Dat T. Tran
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2610.00893
UR  - https://arxiv.org/abs/2610.00893
AB  - 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.
ER  -