# Math Help - prove(easy for you all):

1. ## prove(easy for you all):

if $2^p-1$ is prime prove that p is also a prime

2. The typical way is to prove the contrapositive: If $n$ is composite, i.e. $n = ab$, then $2^{n} - 1$ is composite.

Then notice that: $2^{n} - 1 = 2^{ab}-1 = (2^a-1)\left(2^{a(b-1)} + 2^{a(b-2)} + \cdots + 2^{a} + 1\right)$