  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.
