On primitive integer solutions of the Diophantine equation x³± y³=a^k± b^k

2024/02/09 by Maciej Ulas, Ulas, Maciej
Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Algebraic Geometry and Number Theory #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2402.06567

openalex publication_date 2024/02/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note we consider the title Diophantine equation from both theoretical as well as experimental point of view. In particular, we prove that for k=4, 6 and each choice of the signs our equation has infinitely many co-prime positive integer solutions. For k=5, 7 and all choices of the signs we computed all co-prime positive integer solutions (x, y, a, b) satisfying the condition \opmax\a, b\≤ 50000.

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