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Prove by induction. a ) If a, n ∈ N and a∣n then a ≤ n....

Prove by induction.

a ) If a, n ∈ N and a∣n then a ≤ n.

b) For any n ∈ N and any set S = {p1, . . . , pn} of prime numbers, there is a prime number which is not in S.

c) Prove using strong induction that every natural number n > 1 is divisible by a prime.

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