Question 53
Let
$$
f(n) = \sum_{k=0}^{2010} n^k = 1 + n + n^2 + \dots + n^{2010}.
$$
Prove that for every integer $m$ with $2 \le m \le 2010$, there is no non-negative integer $n$ such that $f(n)$ is divisible by $m$.
$$
f(n) = \sum_{k=0}^{2010} n^k = 1 + n + n^2 + \dots + n^{2010}.
$$
Prove that for every integer $m$ with $2 \le m \le 2010$, there is no non-negative integer $n$ such that $f(n)$ is divisible by $m$.