Let $B(n)$ denote the Bell's number which is the number of the equivalence relation which can be defined on a set of cardinality $n$.

While I was trying to solve a problem, I reached another result;

$$B(p^k)\equiv k+1 \ mod \ p$$

Is this result evident or trivial ? Any comments and remark are welcome.

Note: My field is not Number theory, that is why I am not famialiar with the tools and result in number theory. If this question is something trivial, please excuse me.