# Bézout's identity

### URI(s)

- http://id.loc.gov/authorities/subjects/sh2007006114
- info:lc/authorities/sh2007006114
- http://id.loc.gov/authorities/sh2007006114#concept

### Instance Of

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### Variants

- Bézout identity
- Bézout's lemma

### Broader Terms

### Closely Matching Concepts from Other Schemes

### Sources

- found: Work cat.: Lawton, W.M. Bézout identities with inequality constraints, 1998.
- found: Wikipedia, July 31, 2007(Bézout's identity or Bézout's lemma is a linear diophantine equation. It states that if a and b are nonzero integers with greatest common divisor d, then there exist integers x and y (called Bézout numbers or Bézout coefficients) such that ax + by = d)
- found: MathWorld, via WWW, July 31, 2007(Bézout's identity -- If a and b are integers not both equal to 0, then there exist integers u and v such that GCD (a, b) = au + bv, where GCD (a, b) is the greatest common divisor of a and b)
- found: Fermat's last theorem : Bezout's identity for Gaussian integers, via WWW, July 31, 2007(Bezout's identity states that the greatest common denominator of any two integers can be expressed as a linear combination with two other integers)
- found: Glossary of mathematical terms, via WWW, July 31, 2007(Euclid's algorithm ... The generalization of the Corollary [for Euclid's algorithm] to an arbitrary field is known as Bézout's identity or Bézout's Lemma ...)
- notfound: James, R.C. Mathematics dictionary, 1992;The Penguin dictionary of mathematics, 1989;Dictionary of applied math for engineers and scientists, 2003;Encyclopedic dictionary of mathematics, 1987

### Change Notes

- 2009-10-23: new

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