Bezout's Identity states that for any two integers, there exist integers x and y such that the two integers multiplied by x and y respectively and added together equal the greatest common divisor of the two original integers. Named for Etienne Bezout, it is a basic result of elementary number theory whose witnessing values are computed in practice by the extended Euclidean algorithm.
Facts
StatementBezout's Identity states that for any two integers a and b with greatest common divisor d, there exist integers x and y, called Bezout coefficients, such that a times x plus b times y equals d; the same identity extends to give the greatest common divisor of any finite list of integers as an integer linear combination of them. 1 Classification
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Source Bezout's Identity (Wikipedia)
Sources
1. Bezout's Identity (Wikipedia)
Wikimedia FoundationHistory section
The French mathematician Étienne Bézout (1730-1783) proved this identity for polynomials. The statement for integers can be found already in the work of an earlier French mathematician, Claude Gaspard Bachet de Méziriac (1581-1638).
Proved By: Étienne Bézout, Lead
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.
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