An integer n is divisible by k e Z when there exists another integer m satisfying n = Integers that divide n are called factors. A proper factor k dividing n satisfies 0 < k < n. A perfect number is an integer n > 0 that can be written as the sum of its proper factors. For example, the number 14 is not perfect: the set of proper factors of 14 are {1,2,7}, but 1+2+7= 107 14. km. Prove the following statements. (a) At least one perfect number exists. (b) For any prime integer p, the positive integer p? is not a perfect prime.

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