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 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 |