Bézout's Identity
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In number theory, Bézout''s identity or Bézout''s lemma is a linear diophantine equation.Bézout''s identity is named after Étienne Bézout (1730 1783), who proved it for polynomials. However, this statement for integers can be found already in the work of French mathematician Claude Gaspard Bachet de Méziriac (1581 1638).Bézout''s identity works not only in the ring of integers, but also in any other principal ideal domain (PID). That is, if R is a PID, and a an...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In number theory, Bézout''s identity or Bézout''s lemma is a linear diophantine equation.Bézout''s identity is named after Étienne Bézout (1730 1783), who proved it for polynomials. However, this statement for integers can be found already in the work of French mathematician Claude Gaspard Bachet de Méziriac (1581 1638).Bézout''s identity works not only in the ring of integers, but also in any other principal ideal domain (PID). That is, if R is a PID, and a and b are elements of R, and d is a greatest common divisor of a and b, then there are elements x and y in R such that ax + by = d. The reason: the ideal Ra+Rb is principal and indeed is equal to Rd. An integral domain in which Bézout''s identity holds is called a Bézout domain.
