The diophantine equation (2^k-1)(3^k-1)=xⁿ

2025/01/06 by Bo He, He, Bo, Chang Hong Liu +1
Computer Science · Mathematics · #Topological and Geometric Data Analysis #Algebraic Geometry and Number Theory #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2501.04050

Abstract

In this paper, we investigate the Diophantine equation (2^k - 1)(3^k - 1) = xⁿ and prove that it has no solutions in positive integers k, x, n > 2.

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