Find the largest integer $n$ for which $\frac{n^{2007}+n^{2006}+\cdots+n^2+n+1}{n+2007}$ is an integer.
Problem
Source: 2008 Philippine Mathematical Olympiad Problem 2
Tags: number theory unsolved, number theory
Source: 2008 Philippine Mathematical Olympiad Problem 2
Tags: number theory unsolved, number theory
Find the largest integer $n$ for which $\frac{n^{2007}+n^{2006}+\cdots+n^2+n+1}{n+2007}$ is an integer.