I'm working to better understand Bezout coefficients and gcd. I can hand calculate down through the Extended Euclidian Algorithm to calculate the gcd and then gather terms effectively to determine the Bezout coefficients. Until I get to a situation where a divides b evenly with no remainder in gcd(a,b).
I can see that gcd(4,2) is 2 just by inspection as 2 is the largest common divisor. For the Bezout coefficients, I can guess the linear combination would be:
1(4) - 1(2) = 2 =gcd(4,2)
where s=1 and t=1 (minor edits here to fix errors) for the Bezout coefficients. If I use the extended Euclidian algorithm and work back up, I can't since the first line out of the gate has zero as the remainder.
4 = 2(2) + 0
Using the Euclid - Wallis method noted in several posts here, it appears that the Bezout coefficients for gcd(4,2) would be:
1(4) - 2(0)
That seems wrong.
Your assistance in clarifying this is appreciated.