In 28 and 29, for the given values of A and B, make a table showing the value of s, t, and s A + t B before the start of the while loop and after each iteration of the loop.

29. A = 284 ,   B = 168

To calculate:

A table with values s,t and sA+tB before the while loop and after the loop.

Given information:

The given numbers are A=284 and B=168.

Calculation:

Take 0^th iteration, the values are a=A,b=B,s=1,t=0,u=0,v=1.

Note that, sa+tb=1⋅284+0⋅168=284.

Take 1^th iteration of the while-loop.

r=amodb=284mod168=116

q=a div b=284 div 168=1

a=b=168

b=r=116

new u=s−uq=1−0⋅1=1

new v=t−vq=0−1⋅1=−1

s=u=0

t=v=1

u=new u=1

v=new v=−1

sa+tb=0⋅168+1⋅116=116

Take 2^th iteration of the while-loop.

r=amodb=168mod116=52

q=a div b=168 div 116=1

a=b=116

b=r=52

new u=s−uq=0−1⋅1=−1

new v=t−vq=1−(−1)⋅1=1+1=2

s=u=1

t=v=−1

u=new u=−1

v=new v=2

sa+tb=1⋅116+(−1)⋅52=−6

Take 3^th iteration of the while-loop.

r=amodb=116mod52=12

q=a div b=116 div 52=2

a=b=52

b=r=12

new u=s−uq=1−(−1)⋅2=1+2=3

new v=t−vq=−1−2⋅2=−1−4=−5

s=u=−1

t=v=2

u=new u=3

v=new v=−5

sa+tb=(−1)⋅52+2⋅12=6

Take 4^th iteration of the while-loop