\begin{definition}[Definition:Bézout Numbers]
Let $a, b \in \Z$ such that $a \ne 0$ or $b \ne 0$.
Let $d$ be the greatest common divisor of $a$ and $b$.
By Bézout's Lemma:
:$\exists x, y \in \Z: a x + b y = d$
The numbers $x$ and $y$ are known as '''Bézout numbers''' of $a$ and $b$.
\end{definition}