AT-OEMO-FED1 2010 Problem 1

Let $f(n)=\sum_{k=0}^{2010}n^k$ . Show that for any integer $m$ satisfying $2\leqslant m\leqslant 2010$ , there exists no natural number $n$ such that $f(n)$ is divisible by $m$ .

(41st Austrian Mathematical Olympiad, National Competition, part 1, Problem 1)