Bezout Coefficients Calculator

About this calculator

Bezout's identity states that for any integers a and b, there exist integers x and y — the Bezout coefficients — satisfying ax + by = gcd(a, b). This calculator finds x, y and the GCD using the extended Euclidean algorithm, which runs the ordinary GCD algorithm forward while tracking the coefficients backward through each remainder step.

Beyond number theory, Bezout coefficients are the standard way to compute a modular multiplicative inverse — essential in RSA and other cryptographic key generation — and they underlie solving linear Diophantine equations of the form ax + by = c.