Answer:
1. gcd(77,30)=1
Since 1 is the last non zero remainder appearing in these equations then, 1 is the gcd of 77 and 30.
2. u=-11, v=18
Using the Euclidean Algorithm we have that
Now, we express the remainder as linear combinations of 49 and 30.
Then
3. x=18
If then
for some
.
Then, if k=7,