English

Multiplicative dependence in linear recurrence sequences

Number Theory 2026-01-14 v1

Abstract

For a wide class of integer linear recurrence sequences (u(n))n=1\left(u(n)\right)_{n=1}^\infty, we give an upper bound on the number of ss-tuples (n1,,ns)(Z[M+1,M+N])s\left(n_1, \ldots, n_s\right) \in \left(\mathbb Z\cap [M+1,M+ N]\right)^s such that the corresponding elements u(n1),,u(ns)u(n_1), \ldots, u(n_s) in the sequence are multiplicatively dependent.

Keywords

Cite

@article{arxiv.2501.17365,
  title  = {Multiplicative dependence in linear recurrence sequences},
  author = {Attila Bérczes and Lajos Hajdu and Alina Ostafe and Igor E. Shparlinski},
  journal= {arXiv preprint arXiv:2501.17365},
  year   = {2026}
}
R2 v1 2026-06-28T21:23:05.798Z