Say I have beads of $5$ colours, White, Yellow, Red, Green and Blue. I want to create a necklace of length $17$. How many unique necklaces can I create? (Up to rotation and reflection. For example, if the length was just 3, RGB and RBG should be identical)
The main problem I was facing was I could not choose a "uniform" factor to divide with. There are way too many different cases. Any tips/hints? I'm not even sure if this can be done via elementary combinatorics only.