\(2^m+2^n=2^{m+n}<=>2^m+2^n-2^m-2^n=0\)
\(\Leftrightarrow2^m\left(2^n-1\right)-\left(2^n-1\right)=1<=>\left(2^n-1\right)\left(2^m-1\right)=1\)
\(\Leftrightarrow\int^{2^n-1=1}_{2^m-1=1}=>m=m=1\)
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