Bézout coefficients

Bézout coefficients are integers that provide a way to express the greatest common divisor (GCD) of two integers as a linear combination of those integers. Specifically, for two integers \( a \) and \( b \), the GCD can be written as: \( \text{GCD}(a, b) = ax + by \), where \( x \) and \( y \) are the Bézout coefficients. This concept is useful in number theory and has applications in areas like cryptography and solving Diophantine equations, where finding integer solutions is important. Essentially, Bézout coefficients show how two numbers can combine to form their greatest common divisor.