Given two positive integers $a$ and $b$, Bezout's identity state that there exist integers $x$ and $y$ such that \[ax+by=\gcd(a,b)\] The integers $x$ and $y$ are called Bezout coefficients. This calculator calculate $x$ and $y$ using the extended Euclidean algorithm. Note that if $\gcd(a,b)=1$ we obtain $x$ as the multiplicative inverse of $a$ modulo $b$: \[ ax\equiv 1\mod{b} \] If $x$ is negative, just add $b$ to it until it get positive value.

Bezout Coefficients Calculator