Statement

Let $a,b,m$ be three integers such that $m > 1$ and $a \neq 0$ . We are interested in solving in ${\mbox{${\mathbb{Z}}$}}/m{\mbox{${\mathbb{Z}}$}}$ the equation

$$a x =\ b$$ (1)

Let $g$ be the gcd of $a$ and $m$ in ${\mathbb{Z}}$ .