There are many important facts that go along with Bezout’s identity:

1.)    All common divisors of \(d\) are common divisors of \(a\) and \(b\) as well
2.)    As for the fact above, all divisors of \(a\) and \(b\) are also divisors of \(d\)
3.)    \(a\)/\(d\) and \(b\)/\(d\) are prime integers
4.)    \(a\)/\(d\)\(\left(x\right)\)+\(b\)/\(d\)\(\left(y\right)\)\(=1\)
5.)    The greatest common divisor \(d\) is actually the smallest integer that can be written to satisy \(ax+by\)
6.)    All integers of the form \(ax+by\) are multiples of \(d\)