An elementary proof of a result Ma and Chen

2019/03/01 by Qing Han, Pingzhi Yuan, Han, Qing +1
Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1903.00121

arxiv created 2019/03/01 · openalex publication_date 2019/03/01 · arxiv updated 2019/03/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In 1956, Je\acutesmanowicz conjectured that, for positive integers m and n with m>n, gcd(m, n)=1 and m\not≡ n\pmod2, the exponential Diophantine equation (m²-n²)^x+(2mn)^y=(m²+n²)^z has only the positive integer solution (x, y, z)=(2, 2, 2). Recently, Ma and Chen \citeMC17 proved the conjecture if 4\not|mn and y≥2. In this paper, we present an elementary proof of the result of Ma and Chen \citeMC17.

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