On the equation x²-2^m=yⁿ

2020/08/26 by Lucas Villagra Torcomian, Torcomian, Lucas Villagra
Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2008.11515

openalex publication_date 2020/08/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article we finish the study of solutions of the equation x²-2^m=yⁿ for m∈ℤ and n≥3. This is achieved using the modularity method in unsolved cases, namely, we prove that the only integer solutions of x²-2=yⁿ for n≥2 are (±1,-1) when n is odd.

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