# One problem about number theory

## Homework Statement

Let $$p\ge 2$$. Prove if $$2^p-1$$ is prime, then $$p$$ must be prime.

## The Attempt at a Solution

I am a physics student. I need help from those studying mathematics. Thank you very much!

Try to find a factorization of $$2^{ab}-1=(2^a)^b-1$$...
(HINT: what does $$x^n-y^n$$ equal?)