(adsbygoogle = window.adsbygoogle || []).push({}); 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!

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# Homework Help: Fermat's little theorem

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