Let $a,b \in \mathbb{Z}$ be not both zero, and let $\gcd(a,b)$ denote their positive [greatest common divisor](/page/Greatest%20Common%20Divisor). Then $a$ and $b$ are coprime, meaning $\gcd(a,b)=1$, if and only if there exist $x,y \in \mathbb{Z}$ such that