# Bezout Identity (Bezout Lemma)

** Published:**

$gcd(a,b)=d$ $\Leftrightarrow$ $\exists x,y \in \mathbb{Z}, s.t., ax+by=d$

# Statement

Let a and b be integers with greatest common divisor d. Then, there exist integers x and y such that ax + by = d. More generally, the integers of the form ax + by are exactly the multiples of d.