9. Given that $m, n$ are positive integers, where $n$ is odd, find the greatest common divisor of $2^{m}+1$ and $2^{n}-1$.

 untranslated portion:
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Given $n$ is odd $\Rightarrow\left(2^{m}+1\right)\left|\left(2^{m n}+1\right),\left(2^{n}-1\right)\right|\left(2^{m n}-1\right)$, then $\left(2^{m}+1,2^{n}-1\right) \mid\left(2^{m n}+1,2^{m n}-1\right)=\left(2,2^{m n}-1\right)=1$, so $\left(2^{m}+1,2^{n}-1\right)=1$.