The cycle structure of the permutation $a \mapsto ma \bmod{n}$

Given a weird $n$, and also an $m$ such that $(n,m)=1$, i would love to recognize what is the cycle framework of the permutation $\pi_{n,m} (a)=ma\bmod{n}$.

Especially, just how do i recognize if $\pi_{n,m}$ and also $\pi_{n,k}$ have the very same framework.

A lot more especially, do $\pi_{n,m}$ and also $\pi_{n,m^{-1}}$ have the very same framework, when $m\cdot{m^{-1}}=1\bmod{n}$.

Many thanks!

2022-06-07 14:35:31
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Answers: 1

Those last 2 permutations are inverted per various other, no? What do you find out about the cycle framework of a permutation and also its inverted?

2022-06-07 14:58:33