Let a disk be divided in \(p\) equal sectors, where \(p\) is prime, and colored with \(n\) colors. Two colorations which can be deduced one from the other by rotating the disk around its center in some direction, are not considered distinct. We can use the same color in all sectors. In how many ways can this be done?
For answering, take \(n=4\) and \(p=3\)
This problem was inspired on some USSR Olympiad problems