I have this math question that I am stuck on. This is the question:
Suppose that $a$ and $b$ are positive integers, with $d = \gcd(a, b)$. Suppose that there exists integers $r$ and $s$ so that $ar + bs= d$. Show that $\gcd(r, s) = 1$ using the relatively prime equation.
This is the relatively prime relationship equation: Let $a,b$ be non-zero integers. $a$ and $b$ are relatively prime iff there exists integers $x$ and $y$ such that $ax+by=1$
I know that the relatively prime equation that I have to solve is $ar + bs = 1$. However, I'm not sure how to start this. Thanks.