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Let $m, n\geq 1$ be integers.

Which of the following statements are true? Select ALL that apply.

If $2^n-1$ is a prime number, then $n$ is prime.

If $2^m+1$ is a prime number, then $m$ is prime.

If $2^n-1$ is a prime number, then $n=2^k$ for some integer $k\geq 0$.

If $2^m+1$ is a prime number, then $n=2^k$ for some integer $k\geq 0$.