Given an unlimited number of beads of n different types, how many circular necklaces are there, with the length of p (a prime number), that can be created by connecting the beads together?
Note that two necklaces are identical if we can get one of the necklaces by rounding the other necklace.
I have an approach; First we count how many necklaces there to exist with the length of p and of n different beads and then we divide all the possibilities by the number of equivalence classes. I believe that there are 360/p different equivalence classes.
I am not certain whether this is the right approach, and also is this the right number of equivalence classes?
Disclaimer: I am asking this question for a friend who does not know how to use this site and cannot formulate a question that is comprehensible in English, so I apologize for any vague point.