Let p be a prime number. Find a formula, in terms of p only, for the number of all
irreducible polynomials of degree 20 in Zp[x]

I think means that we are looking for the number of Galois fields, this number is
\frac{1}{d}\sum_{d|m}\mu(\frac{d}{m})p^m
where here d = 20, and \mu is the Mobius Function
but does this mean?
and how does it help?