 This may be seen by multiplying Bézout's identity by "m",

Therefore, the set of all numbers "ua" + "vb" is equivalent to the set of multiples "m" of "g".In other words, the set of all possible sums of integer multiples of two numbers ("a" and "b") is equivalent to the set of multiples of gcd("a", "b").The GCD is said to be the generator of the ideal of "a" and "b".