PMO 2008 Problem 2

Find the largest integer $n$ for which $\frac{n^{2007}+n^{2006}+\cdots+n^2+n+1}{n+2007}$ is an integer.

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.