I am trying to find a solution to $823x + 4526y = 1$ using the Euclidean Algorithm.
Here is what I have so far, but I am doing something wrong because the answers don't work.
$823x\ +\ 4526y=1$
$4526\ =\ 823\ \cdot\ 5\ +\ 411$
$823\ =\ 411\ \cdot2\ +\ 1$
$411\ =\ 1\ \cdot411\ +\ 0$
Rewriting as Remainders
$411=4526\ +\ -5\ \cdot823$
$1=823\ +\ -2\ \cdot411$
Plug in
$1 =823 +-2 \cdot 4526 + -5 \cdot 823$
$x = -2$ and $y=-4$