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a) Prove that if p is prime and 0 < k < p, then (p choose k ) = p! k!(pk)! is divisible by p.
a) Prove that if p is prime and 0 < k < p, then (p choose k ) = p! k!(pk)! is divisible by p.
b) Use part a) to prove that (a + b) p = (a p + b p) mod p.
c) Use part b) to show that 2p 2 mod p, then 3p 3 mod p.
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