1st question: Fermat's little theorem: If p is prime and p does not divide a, a E Z, then ap-1 is congruent to 1 mod p. Corollary: For all a E Z and all primes p, ap 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!