Bézout's identity

In mathematics, Bézout's identity (also called Bézout's lemma), named after Étienne Bézout who proved it for polynomials, is a theorem which relates two arbitrary integers with their greatest common divisor. The theorem's statement is as follows:

Bézout's identity—Let a and b be integers with greatest common divisor d. Then there exist integers x and y such that ax + by = d. Moreover, the integers of the form az + bt are exactly the multiples of d.