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Problem

A positive integer, N, is an sum-product number if there exists a set of positive integers:
S = {a₁,a₂,...,a_k}, such that N = a₁ a₂ ... a_k = a₁ + a₂ + ... + a_k. 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.