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arXiv · 2203.07061

On the Skolem Problem for Reversible Sequences

George Kenison
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Abstract

Given an integer linear recurrence sequence $\langle X_n \rangle_n$, the Skolem Problem asks to determine whether there is a natural number $n$ 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.

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George Kenison. 2022-03-14. On the Skolem Problem for Reversible Sequences. https://arxiv.org/abs/2203.07061

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