Tool to compute Bezout coefficients. The Bezout Identity proves that it exists solutions to the equation a.u + b.v = PGCD(a,b).
Bezout's Identity - dCode
Tag(s) : Arithmetics
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Example: $ a=12 $ and $ b=30 $, gcd $ (12, 30) = 6 $. There are multiple solutions to $ u $ and $ v $ such as $ 12u + 30v = 6 $, such as : $$ 12 \times -2 + 30 \times 1 = 6 $$
The dCode Bezout coefficients calculator gives only one solution.
The Bézouts coefficients are the values $ u $ and $ v $.
A source code for the identity of Bezout would be similar to this pseudo-code:
Initialization r = a, r' = b, u = 1, v = 0, u' = 0 and v' = 1
While (r' != 0)
q = (int) r/r'
rs = r, us = u, vs = v,
r = r', u = u', v = v',
r' = rs - q*r', u' = us - q*u', v' = vs - q*v'
Return (r, u, v)