Bezout’s lemma (number theory)

Let $a,b$ be integers, not both zero. Then there exist two integers $x,y$ such that:

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

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

Title	Bezout’s lemma (number theory)
Canonical name	BezoutsLemmanumberTheory
Date of creation	2013-03-22 12:40:40
Last modified on	2013-03-22 12:40:40
Owner	mathwizard (128)
Last modified by	mathwizard (128)
Numerical id	10
Author	mathwizard (128)
Entry type	Theorem
Classification	msc 11A05
Synonym	Bezout’s lemma
Synonym	Bezout’s theorem
Related topic	EuclidsAlgorithm
Related topic	EuclidsCoefficients
Related topic	GreatestCommonDivisorOfSeveralIntegers