Explanation 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, s a + t b = 1 ⋅ 284 + 0 ⋅ 168 = 284 . Iteration 0 a 284 b 168 r q s 1 t 0 u 0 v 1 new u new v s a + t b 284 Take 1 th iteration of the while-loop. r = a mod b = 284 mod 168 = 116 q = a div b = 284 div 168 = 1 a = b = 168 b = r = 116 n e w u = s − u q = 1 − 0 ⋅ 1 = 1 n e w v = t − v q = 0 − 1 ⋅ 1 = − 1 s = u = 0 t = v = 1 u = n e w u = 1 v = n e w v = − 1 s a + t b = 0 ⋅ 168 + 1 ⋅ 116 = 116 Iteration 0 1 a 284 168 b 168 116 r 116 q 1 s 1 0 t 0 1 u 0 1 v 1 − 1 new u 1 new v − 1 s a + t b 284 116 Take 2 th iteration of the while-loop. r = a mod b = 168 mod 116 = 52 q = a div b = 168 div 116 = 1 a = b = 116 b = r = 52 n e w u = s − u q = 0 − 1 ⋅ 1 = − 1 n e w v = t − v q = 1 − ( − 1 ) ⋅ 1 = 1 + 1 = 2 s = u = 1 t = v = − 1 u = n e w u = − 1 v = n e w v = 2 s a + t b = 1 ⋅ 116 + ( − 1 ) ⋅ 52 = − 6 Iteration 0 1 2 a 284 168 116 b 168 116 52 r 116 52 q 1 1 s 1 0 1 t 0 1 − 1 u 0 1 − 1 v 1 − 1 2 new u 1 − 1 new v − 1 2 s a + t b 284 116 64 Take 3 th iteration of the while-loop. r = a mod b = 116 mod 52 = 12 q = a div b = 116 div 52 = 2 a = b = 52 b = r = 12 n e w u = s − u q = 1 − ( − 1 ) ⋅ 2 = 1 + 2 = 3 n e w v = t − v q = − 1 − 2 ⋅ 2 = − 1 − 4 = − 5 s = u = − 1 t = v = 2 u = n e w u = 3 v = n e w v = − 5 s a + t b = ( − 1 ) ⋅ 52 + 2 ⋅ 12 = 6 Iteration 0 1 2 3 a 284 168 116 52 b 168 116 52 12 r 116 52 12 q 1 1 2 s 1 0 1 − 1 t 0 1 − 1 2 u 0 1 − 1 3 v 1 − 1 2 − 5 new u 1 − 1 3 new v − 1 2 − 5 s a + t b 284 116 64 − 28 Take 4 th iteration of the while-loop

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Chapter 8.4, Problem 29ES

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

Solution Summary: The author calculates a table with values s,tandsA+tB before the while loop and after the loop.

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

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

Solution Summary: The author calculates a table with values s,tandsA+tB before the while loop and after the loop.

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

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Chapter 8 Solutions

To calculate:

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