On the Skolem Problem for Reversible Sequences

03/14/2022

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by   George Kenison, et al.

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Given an integer linear recurrence sequence ⟨ X_n ⟩_n, the Skolem Problem asks to determine whether there is a natural number n such that X_n = 0. In a recent preprint, Lipton, Luca, Nieuwveld, Ouaknine, Purser, and Worrell prove that the Skolem Problem is decidable for a class of reversible sequences of order at most seven. Herein, we give an alternative proof of the result. The novelty of our approach arises from our use of results concerning the polynomial relations between Galois conjugates.