Originally Posted by

**clic-clac** Hi

Of course there is a way: let $\displaystyle n$ be an integer, the generators of $\displaystyle \mathbb{Z}_n$ are the classes of integers which are relatively prime with $\displaystyle n,$ i.e. $\displaystyle \{[x]\in\mathbb{Z}_n;\ gcd(x,n)=1\}$

That comes from Bezout relation: $\displaystyle gcd(x,n)=1\Rightarrow \exists u,v\in\mathbb{Z},\ ux+vn=1 \Rightarrow [u][x]=[1]$ so $\displaystyle [x]$ is a generator.

Conversely, $\displaystyle [x]$ generator $\displaystyle \Rightarrow \exists u\in\mathbb{N},\ [u][x]=1\Rightarrow \exists u,v\in \mathbb{Z},\ ux=1-vn$