Proof of Fermat's Little Theorem: g Generator of Fp*

jacquelinek
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Prove that:
g is a generator of Fp* if and only if g^(p-1) = 1 (mod p) and gq ≠ 1 (mod p) for all prime divisors q of (p – 1).

I am thinking about applying Fermat's theorem...but don't know how...
Request help, thanks.
 
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Should that be gq?

Fermat's theorem may be useful for part of the proof. It certainly cannot prove this theorem all by itself.

What do you know about finite fields? And about their unit groups?
 

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