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A Universal Skolem Set of Positive Lower Density

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.