Extended Euclidean Algorithm: Stuck on "compute gcd(3213,234)"

[hanspeter]

Hi,

I'm stuck at the end of the extended euclidean algorithm.

The task is "Calculate the greatest common divisor gcd(3213,234) using the euclidean algorithm and find s, t ∈ Z such that s · 3213 + t · 234 = gcd(3213, 234)"

Here's a PDF of what I've done: https://owncloud.mafiasi.de/index.php/s/SlmTUmUahVrIQWA (think gcd where it says ggT, that's German for gcd)

gcd(3212,234) = 9 so I need to find s, t ∈ Z such that s · 3213 + t · 234 = 9.

I have 3 · 3213 - 39 · 234 -504 = 9. How do I now get rid of the -504? I can't for the life of me find a solution. :/

Thanks

(Please excuse all the stuff I've probably spelled incorrectly, English is not my native language.)

 

[hanspeter]

A friend already caught my mistake. The second to last line should be 3 * 171 - 8 * (234 - 1 * 171).

Then the result is 11 * 2313 - 151 * 234 = 9.
s=11, t=-151