If $p$ is a prime, and $d$ is an integer greater than or equal to 1.
Let $n= p^d$, then there exists $K$ being a field of order $p^n$.
But how many different proper subfields does $K$ have?
The following property might be helpful, though I can't find a proof for it.
Say if $F$ is a subfield of $K$, then $F$ has order $p^d$ for some $d$ such that $d \ | \ n$.
Thanks in advance!