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In 1956, Je$acute{s}$manowicz conjectured that, for positive integers $m$ and $n$ with $m>n, , gcd(m,, n)=1$ and $m otequiv npmod{2}$, 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 $4 ot|mn$ and $yge2$. In this paper, we present an elementary proof of the result of Ma and Chen cite{MC17}.
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