Question

Use the Euclidean's Algorithm to obtain the integers x and y satisfying this​

Answer 1

Answer:

so x=-5, y= -217, z = 124

Step-by-step explanation:

Apply Euclid' div lemma on 512 and 288

512=288+224

so 224=512-288---------------(1)

288=224+64

64=288-224------------------(2)

224=64*3+32

32=224-64*3-------------(3)

64=32*2+0

so GCD(512,288)=32

Now Apply Euclid' di lemma on 32 and 198

198=32*6+6

6=198-32*6-------------------(4)

32=6*5+2

6=2*3+0

so GCD (198,288,512)=2

Now 2=32-6*5

=32-5*( 198-32*6)                from (4)

=32*31-5*198

=(224-64*3)*31 - 5*198                from(3)

=31*[224-(288-224)*3] - 5*198             from(2)

=31*[224*4-288*3]  - 5*198

=31*[ (512-288)*4-288*3]-5*198                  from(1)

=31*(512*4-288*7)-5*198

=124*512 - 217*288 -5*198

2= -5*198-217*288+124*512...................(5)

GCD=198x+288y+512z

so x=-5, y= -217, z = 124