eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2022-08-22
73:1
73:12
10.4230/LIPIcs.MFCS.2022.73
article
A Universal Skolem Set of Positive Lower Density
Luca, Florian
1
2
3
4
https://orcid.org/0000-0003-1321-4422
Ouaknine, Joël
4
https://orcid.org/0000-0003-0031-9356
Worrell, James
5
https://orcid.org/0000-0001-8151-2443
School of Mathematics, University of the Witwatersrand, Johannesburg, South Africa
Research Group in Algebraic Structures & Applications, King Abdulaziz University, Saudi Arabia
Centro de Ciencias Matemáticas UNAM, Morelia, Mexico
Max Planck Institute for Software Systems, Saarland Informatics Campus, Germany
Department of Computer Science, University of Oxford, UK
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 .
https://drops.dagstuhl.de/storage/00lipics/lipics-vol241-mfcs2022/LIPIcs.MFCS.2022.73/LIPIcs.MFCS.2022.73.pdf
Linear Recurrence Sequences
Skolem Problem
Exponential Diophantine Equations
Sieve Methods