Let R be a Principal Ideal Domain. Let a,b \in R, at least one of which is non-zero. Determine precisely all solutions (s,t), where s,t \in R, of the equation sa+tb= \gcd (a,b).
My attempt: since \gcd (a,b) divides both a and b, we can divide both sides by \gcd (a,b) to get the equation s...