Let $d$ and $n$ be coprime. What is the smallest positive solution for x in the equation:
$$d^x \equiv 1 \mod n$$
This value must depend on both $d$ and $n$. We know that the maximum value for it is $\lambda(n)$ where $\lambda$ is the Carmichael function, but the exact value can be smaller. The question can be alternatively phrased as:
Let $d$ and $n$ be coprime. What is the order of the group generated by $d$ under multiplication modulo $n$?
