Also known as Bézout's lemma
formula relating two numbers and their greatest common divisor
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.
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