To prove a property of greatest common divisor Suppose integer $d$ is the greatest common divisor of integer $a$ and $b$,
how to prove, there exist whole number $r$ and $s$, so that 
$$d = r \cdot a + s \cdot b $$
?
i know a proof in abstract algebra, hope to find a number theory proof?
for abstract algebra proof, it's in Michael Artin's book "Algebra".

You can use any textbook on Number Theory, e.g.,  H.Stark, An Introduction to Number Theory, Theorem 2.2.
