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Bézout's identity
Relating two numbers and their greatest common divisor
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: (The greatest common divisor of 0 and 0 is taken to be 0.) The integers x and y are called Bézout coefficients for (a, b); they are not unique. The extended Euclidean algorithm can be used to compute a minimal pair of Bézout coefficients, meaning they satisfy | x | ≤ | b / d | {\displaystyle |x|\leq |b/d|} and | y | < | a / d | {\displaystyle...
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