I was curious about this question:
Let $p$ be a prime, and $d \geq 1$ and $K$ is a field of $p^d$. How many proper subfields does $K$ have?
All I know if that a finite field has order $p^n$, where $p$ is the characteristicc of $K$ and $n:[K:\mathbb{Z}_p]$. But not sure how that helps find the amount of subfields.