Question

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

Answer 1

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

Answer 2

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

Answer 3

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?

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

try below :

x = 3-13k
y = -5 + 22k

Answer 8

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

Answer 9

:P