Determine whether the statement is true or false.
-$\text { If } 2 ^ { n } - 1 \text { is prime, then } 2 ^ { n - 1 } \left( 2 ^ { n } - 1 \right) \text { is perfect. }$

Question

Quizplus · Accepted Answer

If $2^n - 1$ is prime (making it a Mersenne prime), then $2^{n-1}(2^n - 1)$ is a perfect number according to the definition of even perfect numbers discovered by Euclid.

Determine Whether the Statement Is True or False If 2n−1 is prime, then 2n−1(2n−1) is perfect. \text { If } 2 ^ { n } - 1 \text { is prime, then } 2 ^ { n - 1 } \left( 2 ^ { n } - 1 \right) \text { is perfect. } If 2n−1 is prime, then 2n−1(2n−1) is perfect.

Determine Whether the Statement Is True or False $\text { If } 2 ^ { n } - 1 \text { is prime, then } 2 ^ { n - 1 } \left( 2 ^ { n } - 1 \right) \text { is perfect. }$