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Number Theory

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Fermat and Mersenne Prime Facts: True/False

NUMTH-KRSTZA

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

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

A

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

B

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

C

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

D

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