I am trying to do an exercise that asks me to calculate the numer of irreducible polynomials of degree $12 $ over $\mathbb{F}_p$.
The exercise have 3 parts and I have done the first two parts that askd me to find drew the field diagram from $\mathbb{F}_p$ to $\mathbb{F}_{p^12}$ (that is these two fields and their subfields and the connection between those subfields), in part $b$ I showed that the number of primitive elements of the extension is $p^{12}-p^{4}-p^{6}+p^{2}$.
Can someone please help me with the last part of the exercise ? I tried finding the connection between the number I have found on part $b$ and the numer of irreducible polynomials (of degree $12 $ over $\mathbb{F}_p$) and failed.
Also, I know that there's something called "Moebius inversion formula" that can be of help, but I did not study it and since this isn't a general question I would rather not resort to using it.