PlanetMath: Bezout's lemma (number theory)

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Bezout's lemma (number theory)

(Theorem)

Let be integers, not both zero. Then there exist two integers such that:

$\displaystyle ax+by=\gcd(a,b).$

This does not only work on $\mathbb{Z}$ but on every integral domain where an Euclidean valuation has been defined.

"Bezout's lemma (number theory)" is owned by mathwizard.

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Other names:

Bezout's lemma, Bezout's theorem

Attachments:: proof of Bezout's Theorem (Proof) by Thomas Heye
corollary of Bézout's lemma (Theorem) by pahio

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Cross-references: Euclidean valuation, integral domain, integers
There are 7 references to this entry.

This is version 7 of Bezout's lemma (number theory), born on 2002-05-27, modified 2004-02-13.
Object id is 2954, canonical name is BezoutsLemma.
Accessed 11164 times total.

Classification:

11A05 (Number theory :: Elementary number theory :: Multiplicative structure; Euclidean algorithm; greatest common divisors)

Pending Errata and Addenda

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