[[Examples of groups]]
# Multiplicative group of integers modulo $n$

For any positive integer $n \in \mathbb{N}$, the **multiplicative group of integers modulo $n$** $\mathbb{Z}_{n}^\times$ consists of all positive integers coprime with $n$, #m/def/group 
i.e.
$$
\begin{align*}
\mathbb{Z}_{n}^\times = \{ x \in \mathbb{Z}_{n} : \gcd(x,n) = 1 \}
\end{align*}
$$
which is the [[Group of units]] of the [[Ring of integers modulo 𝑛]]. 

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