A universal Skolem set of positive lower density - Luca, F; Ouaknine, J; Worrell, J (Schloss Dagstuhl – Leibniz-Zentrum für Informatik, 2022)
The Skolem Problem asks to decide whether a given integer linear recurrence sequence (LRS) has a zero term. Decidability of this problem has been open for many decades, with little progress since the 1980s. Recently, a new approach was initiated via the notion of a Skolem set - a set of positive integers relative to which the Skolem Problem is decidable. More precisely, 𝒮 is a Skolem set for a class ℒ of integer LRS if there is an effective procedure that, given an LRS in ℒ, decides whether the sequence has a zero in 𝒮. A recent work exhibited a Skolem set for the class of all LRS that, while infinite, had density zero. In the present work we construct a Skolem set of positive lower density for the class of simple LRS .