## 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 (*u*_{n}),
whether there exists an *n* ∈ **N** such that
*u*_{n} = 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* = *l**p*^{k}, with
*k*, *l* ≤ *c*
and *p* any prime number, such that *u*_{n} = 0.

*Proceedings of ISSAC 20*, 2020. 8 pages.

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