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 \(ax+by=d\).