Universal Skolem Sets
Florian Luca, Joël Ouaknine, James Worrell · 2021
It is a longstanding open problem whether there is an algorithm to decide the Skolem Problem for linear recurrence sequences, namely whether a given such sequence has a zero term. In this paper we introduce the notion of a Universal Skolem Set: an infinite subsetSof the positive integers such that there is an effective procedure that inputs a linear recurrence sequence u = (u(n))n ≥ 0and decides whether u(n) = 0 for some n ∈S. The main technical contribution of the paper is to exhibit such a set.