Calculate gcd(77, 30) by using the euclidean algorithm. find also integers u and v such that 49u + 30v = 1. furthermore, find such x ∈ z that 30x ≡ 1 (mod 77).

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,

d

step-by-step explanation:

given

y + 3 = - 4(x - 2) ← distribute the parenthesis

y + 3 = - 4x + 8 ( subtract 3 from both sides )

y = - 4x + 5 → d

15 batches are the most you can make

step-by-step explanation: