BdMO Online Forum

Let $p$ be a prime number. We call a subset $S$ of $\{1,2,\cdots,p-1\}$ "good" if it satisfies the property that for every $x,y\in S, xy\text{ mod }{p}$ is also in $S$. How many "good" sets are there?

Notice that p is congruent to a modulo b, Where 'a' belongs to {1,2,3....,p-1} and b is any positive integer. Also notice that those integer{1,2,3....p-1} are situated in subset S. So, we must find a subset S for every p.

ig it may have something to do with primitive roots

It's graph theory.