## Sum Product Numbers

#### Problem

A positive integer, N, is an sum-product number if there exists a set of positive integers:

S = {`a`_{1},`a`_{2},...,`a`_{k}}, such that N = `a`_{1} `a`_{2} ... `a`_{k} = `a`_{1} + `a`_{2} + ... + `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.

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