My LCG has the form:
$$S_0 = k$$ $$S_{n+1} = S_n \times a + 1 \pmod m$$
Each choice of $k$ generates a different sequence but in some cases a sequence may just be a cyclic shift of another. In this case we say the two sequences are equivalent. This equivalence partitions the generator outputs into disjoint subsets, or cycle sets.
How many cycle sets are there for a given $a$ and $m$, and how many elements are in each one? Can I also find a representative element for each set? It does not seem practical to find the answer for large $m$ by a brute force search.
