Moderate# Order of a Reduced Residue

ABSALG-252NXG

Let $m\ge 1$ be an integer and let $a$ be any integer coprime to $m$ ($(a,m)=1$).

We define the *order of $a$ mod $m$* to be the smallest positive integer $h$ such that $a^h\equiv 1$ mod $m$. (In some texts this is said as follows: *$a$ belongs to the exponent $h$ mod $m$*.)

Recall that a set $R$ of reduced residues mod $m$ consists of a set $R$ of integers coprime to $m$ that are distinct mod $m$, and such that every integer $a$ coprime to $m$ satisfies $a\equiv r$ for some $r\in R$.

Let $R$ be a set of reduced residues mod $12$.

Which of the following is **TRUE**?

Select **ALL** that apply.