Bézout's identity
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formula relating two numbers and their greatest common divisor
Wikidata facts
- Instance of
- theorem
- Named after
- Claude Gaspar Bachet de Méziriac
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- maintained by WikiProject
- WikiProject Mathematics
- studied by
- number theory
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Encyclopedic overview
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.
Excerpted from Wikipedia’s “Bézout's identity” article, available under the CC BY-SA 4.0 licence.