Divisible by what? $1^n+2^n+\ldots+2006^n$ is divisible by : 
$1.~2006$
$2.~2007$
$3.~2008$
$4.~\text{None}$
Please Explain.

For odd $n$, this answer says that the sum is divisible by $\frac{2006\cdot2007}{2}$.
For even $n$, none need be true. For example,
$$
\sum_{k=1}^{2006}k^2=2692751091
$$
which is divisible by none of $2006$, $2007$, or $2008$.
