Redirected from Bezout's identity
For example, the greatest common divisor of 12 and 42 is 6, and we can write
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.
Bézout's identity is named for the 18th century French mathematician Étienne Bézout.
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