On the Skolem Problem for Reversible Sequences

Abstract

Given an integer linear recurrence sequence h X n i ∞ n =0 , the Skolem Problem asks to determine whether there is an n ∈ N 0 such that X n = 0. Recent work by Lipton, Luca, Nieuwveld, Ouaknine, Purser, and Worrell proved that the Skolem Problem is decidable for a class of reversible sequences of order at most seven. Here we give an alternative proof of their result. Our novel approach employs a powerful result for Galois conjugates that lie on two concentric circles due to Dubickas and Smyth.