Hi, I have this question and i'm really struggling.

Show that for any prime p either $\displaystyle 2^{p} - 1$ is prime or $\displaystyle q = 2^{p} - 1$ behaves like a prime with respect to the base 2 ie $\displaystyle 2^{q-1}\equiv{1}$ (mod q)

I know this is to do with Fermat's little theorem. But i dont know where to start. Please can someone give me a clue?

Thanks,

Katy