English

Twisted rational zeros of linear recurrence sequences

Number Theory 2024-01-15 v1

Abstract

We introduce the notion of a twisted rational zero of a non-degenerate linear recurrence sequence (LRS). We show that any non-degenerate LRS has only finitely many such twisted rational zeros. In the particular case of the Tribonacci sequence, we show that 1/31/3 and 5/3-5/3 are the only twisted rational zeros which are not integral zeros.

Cite

@article{arxiv.2401.06537,
  title  = {Twisted rational zeros of linear recurrence sequences},
  author = {Yuri Bilu and Florian Luca and Joris Nieuwveld and Joël Ouaknine and James Worrell},
  journal= {arXiv preprint arXiv:2401.06537},
  year   = {2024}
}

Comments

30 pages

R2 v1 2026-06-28T14:15:11.756Z