# On the Skolem Problem and prime powers

G. Kenison,
R. Lipton,
J. Ouaknine,
J. Worrell

July, 2020

### Abstract

The Skolem Problem asks, given a linear recurrence sequence $(u_n)$, whether there exists $n\in\mathbb{N}$ such that $u_n = 0$. In this paper we consider the following specialisation of the problem: given in addition $c\in\mathbb{N}$, determine whether there exists $n\in\mathbb{N}$ of the form $n = lp^k$, with $k, l \leq c$ and $p$ any prime number, such that $u_n = 0$.

Publication

*International Symposium on Symbolic and Algebraic Computation, ISSAC `20*