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An elementary proof of a result Ma and Chen
- Publication Year :
- 2019
-
Abstract
- In 1956, Je$\acute{s}$manowicz conjectured that, for positive integers $m$ and $n$ with $m>n, \, \gcd(m,\, n)=1$ and $m\not\equiv n\pmod{2}$, the exponential Diophantine equation $(m^2-n^2)^x+(2mn)^y=(m^2+n^2)^z$ has only the positive integer solution $(x,\,y,\, z)=(2,\,2,\,2)$. Recently, Ma and Chen \cite{MC17} proved the conjecture if $4\not|mn$ and $y\ge2$. In this paper, we present an elementary proof of the result of Ma and Chen \cite{MC17}.
- Subjects :
- Mathematics - Number Theory
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1903.00121
- Document Type :
- Working Paper