Theorem Let (R,+,×) be a PID. Let a,b∈R Then, there exists a c,d∈R such tat ca+db=gcd(a,b)) Proof Let a,b∈R Let I be the Ideal genereated by a,b Then, by our previous theorem, g⋅(a,b)∈I Thus, ∃c,d∈R such that ca+db=gcd(a,b)