Multiplicative dependence in linear recurrence sequences

preprint2025arXivOpen access

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.

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