Prove that for any integer $a > 1$ there is a prime $p$ for which $1+a+a^2+...+ a^{p-1}$ is composite.
Problem
Source: 2001 Estonia National Olympiad Final Round grade 12 p4
Tags: Composite, Sum of powers, prime, number theory
Source: 2001 Estonia National Olympiad Final Round grade 12 p4
Tags: Composite, Sum of powers, prime, number theory
Prove that for any integer $a > 1$ there is a prime $p$ for which $1+a+a^2+...+ a^{p-1}$ is composite.