Problem

Source: China Western Mathematical Olympiad 2008

Tags: number theory, number theory proposed



Given an integer $ m\geq$ 2, m positive integers $ a_1,a_2,...a_m$. Prove that there exist infinitely many positive integers n, such that $ a_{1}1^{n} + a_{2}2^{n} + ... + a_{m}m^{n}$ is composite.