Note: "hfc" stands for "highest common factor" and is synonymous with "greatest common divisor"
Show that if $a, b$ are positive integers and $d=hcf(a,b)$, then there are positive integers $s,t$ such that $d=sa-tb$.
This is a problem assigned in my undergrad foundations class. I am unsure of how to proceed. How do I assume that $a,b$ are positive integers in the sense of a proof? Am I using the fact that $d|sa$ or $d|tb$.