Let $\displaystyle n \geq 0$ be an integer and $\displaystyle p$ a prime number. Find a formula for the number of monic polynomials of degree $\displaystyle n$ in $\displaystyle \mathbb{F}_p[x]$ which have no zero in $\displaystyle \mathbb{F}_p.$


Hint:
Spoiler:
If $\displaystyle n < p,$ the formula has no closed form.