What is the fastest way to solve Bezout's identity?

Question

ganeshie8 · Answer

Standard way is to use euclidean gcd algorithm. Congruences make life simple though..

thomas5267 · Answer

I am finding the general solution to 132x+78y=6 yet I couldn't find one.

thomas5267 · Answer

I traced my gcd calculation backwards and got $12\times132-20\times78=24$, which I could divide my whole equation by 4 to get my answer but what went wrong?

ganeshie8 · Answer

Looks good to me, so  $(3, -5)$ is a particular solution ?

ganeshie8 · Answer

and the null solution is $\large \dfrac{t}{6}(-78, 132)$
then the general solution can be given by  $\large   (3, -5) + \frac{t}{6}(-78,132)$

thomas5267 · Answer

x=3-13k, y=-5+21k?  But it doesn't work for k=1.

ganeshie8 · Answer

try below :

x = 3-13k
y = -5 + 22k

thomas5267 · Answer

Wow!  I am astonished by how I can screw up 132/6.

ganeshie8 · Answer

:P