## Polynomials over a Finite Field

Here is a really nice identity.

Let $F = \text{GF}(q)$ where $q$ is a prime power.
Let $M_n$ be the set of of all monic polynomials of degree $n$.
Let $d[f(x)]$ be the number of monic divisors $f(x)\in F[x]$ has.

Then we have the following identity,
$\sum_{f(x)\in M_n} d[f(x)] = (n+1)q^n$