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Sum Product Numbers

Problem

A positive integer, N, is an sum-product number if there exists a set of positive integers:
S = {a1,a2,...,ak}, such that N = a1 times a2 times ... times ak = a1 + a2 + ... + ak. In order for the set to be a sum and product, it is necessary that S contains at least two elements.

Prove that N is a sum-product number iff it is composite.

Problem ID: 200 (10 Jan 2005)     Difficulty: 3 Star

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