Bezout was a famous mathematician who discovered many beautiful formulas. One of his most famous theorem/identities dealt with numbers and their greatest common factors. His theorem states, if integers \(a\) and \(b\) are relatively prime, then there exists \(x\) and \(y\), integers to satisfy the equation \(ax+by=1\). For any integers \(a\) and \(b\) excluding zero, let \(d\) be the greatest common divisor such that \(d\) equals the gcd of \(a\) and \(b\) in other words, \(d\)\(=\)gcd\(\left(a,b\right)\). If this is true then there must exist integers known as \(x\) and \(y\) to satisfy the equation \(ax+by=d\).