It occurred to me just a moment ago that while some mathematical riddles required a certain amount of background (in particular, I was trying to remember if proving there are infinitely many prime numbers is one of those), some don't, and thus make a good brainteaser for the non-mathematician.
Here's a good one. Comments are screened. Impress me!
Prove that (p-1).p.(p+1) must be a multiple of 24.