**Proof:** Before starting with the proof proper, we should observe that although a/d and b/d have the appearance of the functions, in fact, they are integers because *d is a divisor both of a and of b*. Now, knowing that gcd(a, b) = d, it is possible to find integers x and y such that d = ax + by. Upon dividing each side of this equation by d, we obtain the expression

1 = (a/d)x + (b/d)y

Because a/d and b/d are integers, an appeal to the theorem is legitimate. The conclusion is that a/d and b/d are relatively prime.** (Proved)**