Question

Extended euclidean algorithm, find the multiplicative inverse of 1234 mod 4321

Answer 1

Step-by-step explanation:

Hence, the multiplicative inverse of 1234 mod 4321 is -1082.

Answer 2

Answer:

Multiplicative inverse of $1234\ mod\ 4321\ is\ 3239$

Step-by-step explanation:

Multiplicative Inverse of $1234 \bmod 4321=-1082$

$(-1082 * 1234) \bmod 4321=(-1335188) \bmod 4321=$

$4321 *(-308)=-1330868 and 4321 *(-309)=-1335189$

So $-309$ is the greatest multiple less than $1330868$ , so $4321 *-309=-1335189$ and $(-1335188)-(-1335189)=1 ,$showing it's a multiplicative inverse.

To keep the multiplicative inverse confined to the set GF(4321), we can do clockwork arithmetic by saying $4321-1082=3239$. Note that $3239 * 1234=3996926 \bmod 4321=1$, making $3239$ the multiplicative inverse of $1234\ in\ GF(4321)$.