On the Skolem Problem and prime powers

George Kenison, Richard J. Lipton, Joël Ouaknine, and James Worrell

The Skolem Problem asks, given a linear recurrence sequence (un), whether there exists an n ∈ N such that un = 0. In this paper we consider the following specialisation of the problem: given in addition c ∈ N, determine whether there exists n ∈ N of the form n = lpk, with kl ≤ c and p any prime number, such that un = 0.

Proceedings of ISSAC 20, 2020. 8 pages.

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