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A Universal Skolem Set of Positive Lower Density Luca, Florian Ouaknine, Joël Worrell, James Linear Recurrence Sequences Skolem Problem Exponential Diophantine Equations Sieve Methods 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 . Schloss Dagstuhl – Leibniz-Zentrum für Informatik Florian Luca and Joël Ouaknine and James Worrell 2022 Is Part Of LIPIcs, Volume 241, 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.MFCS.2022.73 urn:nbn:de:0030-drops-168711 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2022.73 eng https://creativecommons.org/licenses/by/4.0/legalcode