Use the Sylow Theorems to find the number of prime numbers $p$ and $q$ which satisfy the following conditions:
How would the Sylow Theorems apply to this problem? I'm really confused on how to use them in this setting. This problem just seems like a number theory problem that could be solved using Fermat's Theorem. I genuinely don't understand how to use Sylow $p$-subgroups to solve this problem. Any hints, or explanations would be extremely helpful since I find the Sylow Theorems hard to understand in general.