One problem about number theory

[qinglong.1397]

Homework Statement

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

Homework Equations

The Attempt at a Solution

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

 

[micromass]

Assume that p is NOT prime, then we can write p=ab, with a and b nontrivial.

Try to find a factorization of $$2^{ab}-1=(2^a)^b-1$$...

(HINT: what does $$x^n-y^n$$ equal?)