Consider a sprocket has $s$ teeth, and a chain has $h$ holes. Think about a bicycle chain and the sprocket wheel in the back of the chain.
Sprockets are numbered $0 \ldots s-1$ and holes are numbers $0 \ldots h-1$. We assume $h > s$ and and clearly $s > 1$.
Lets look at discrete time intervals - one sprocket movement is one time unit. At time $t = 0$ we have sprocket $0$ in hole $0$.
What I want to know is at what time $t > 0$ will the $0$ sprocket again find itself to be in the $0$ hole.
I am wondering how would one go about finding an answer for this interesting problem. What kind of mathematics would one use?