Solve each of these congruences using the modular in-verses found in parts (b), (c), and (d) of exercise 6.

a.34x≡77(mod 89)

b.144x≡4(mod 233)

c.200x≡13(mod 1001)

If you've done the aforementioned exercise 6, then you already know

a. In case you don't already have the above, you can use the Euclidean algorithm:

89 = 2*34 + 21

34 = 1*21 + 13

21 = 1*13 + 8

13 = 1*8 + 5

8 = 1*5 + 3

5 = 1*3 + 2

3 = 1*2 + 1

Then we can write 1 as a linear combination of 89 and 34, namely

Taken mod 89, we find that

Then

so that for any integer is a solution to the congruence.

b.

c.

answer: f = 32.2m

step-by-step explanation: that is the answer

30 units^2

step-by-step explanation:

area is l × w

the length is 3

and the width is 10

3 × 10= 30 units squared