15799
Recall that an integer p is prime if p ? 2, and if a, b are positive integers such that p = ab then either a = 1 or b = 1.Theorem. Every integer n ? 2 has a prime factor.One way to prove this for a given integer n ? 2 is to apply the Wellordering Principle to the setX = {d ? Z : d ? 2 ? d | n},the set of all factors d of n such that d ? 2.(a) Prove that X is not empty.(b) Prove that if p is the minimal element of X, then p must be a prime number. (c) Finish the proof of the theorem.Purchase the answer to view it
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