Prime problem, Fermats little theorem?

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$Old$ November 5th, 2009, 10:00 AM

harkapobi $harkapobi is offline$

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$Default$ Prime problem, Fermats little theorem?

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

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

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fermat little theorem, number theory, prime

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