Skolem's conjecture confirmed for a family of exponential equations, II

2021/05/02 by A. Bérczes, L. Hajdu, Bérczes, A. +3
Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2105.00415

openalex publication_date 2021/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

According to Skolem's conjecture, if an exponential Diophantine equation is not solvable, then it is not solvable modulo an appropriately chosen modulus. Besides several concrete equations, the conjecture has only been proved for rather special cases. In this paper we prove the conjecture for equations of the form xⁿ-by₁^k₁… y_ℓ^k_ℓ=± 1, where b,x,y₁,…,y_ℓ are fixed integers and n,k₁,…,k_ℓ are non-negative integral unknowns. This result extends a recent theorem of Hajdu and Tijdeman.

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