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**1st question:**

__Fermat's little theorem:__If p is prime and p does not divide a, a E Z, then a

^{p-1}is congruent to 1 mod p.

__Corollary:__For all a E Z and all primes p, a

^{p}is congruent to a mod p.

I don't really understand the corollary part, why is the assumption "p does not divide a" removed?

I can see why Corollary => Fermat's little theorem,

but I can't see why Fermat's little theorem => Corollary

**2nd question:**

(i) p does not divide a

(ii) a and p are relatively prime

Are (i) and (ii) equivalent? (i.e. (i)=>(ii) and (ii)=>(i) )

Can someone help? Thanks!