Multiplicative dependence in linear recurrence sequences

Abstract

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