Bézout's Identity

Bézout's identity is a concept from number theory that states if you have two integers, say \(a\) and \(b\), there are also two integers, \(x\) and \(y\), such that \(ax + by = d\), where \(d\) is the greatest common divisor of \(a\) and \(b\). This means you can express the greatest common divisor as a combination of \(a\) and \(b\) multiplied by some integers. It highlights a fundamental relationship between numbers that helps in solving equations and understanding their properties.