Bézout's identity

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: (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 |y|<|a/d|} ; equality occurs only if one of a and b is a multiple of the other, and otherwise there exist exactly two minimal pairs.

From Wikipedia, under CC BY-SA. More on occurri.