Definition:Set of Coprime Integers

Definition

Let $n \in \Z$ be an integer such that $n \ge 2$.

Then we define the set $\Z'_n$ as being the set of all integers modulo $n$ which are prime to $n$:

$\Z'_n = \left\{{\left[\!\left[{k}\right]\!\right]_n \in \Z_n: k \perp n}\right\}$

For a prime number $p$, we have that:

$\Z'_p = \Z_p \setminus \left\{{\left[\!\left[{0}\right]\!\right]_p}\right\}$

where $\setminus$ denotes set difference.

That is:

$\Z'_p = \left\{{\left[\!\left[{1}\right]\!\right]_p, \left[\!\left[{2}\right]\!\right]_p, \ldots, \left[\!\left[{p-1}\right]\!\right]_p}\right\}$

This follows from Prime Not Divisor then Coprime.