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(a) Use the Euclidean algorithm to find the greatest common divisor of 21 and 13. Show all your working. (b) The following equations show how we can use the Euclidean algorithm to find the greatest common divisor of 33 and 21. 1 331 x 21 + 12 211 x 12 + 9 12 = 1 x 9 +3 The algorithm shows that gcd (33,21) = 3. Find the integers x and y such that 33x +21y = 3.

(a) Use the Euclidean algorithm to find the greatest common divisor of 21 and 13. Show all your working. (b) The following equations show how we can use the Euclidean algorithm to find the greatest common divisor of 33 and 21. 1 331 x 21 + 12 211 x 12 + 9 12 = 1 x 9 +3 The algorithm shows that gcd (33,21) = 3. Find the integers x and y such that 33x +21y = 3.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.3: Divisibility
Problem 31E
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(a) Use the Euclidean algorithm to find the greatest common divisor of 21 and 13. Show all your working. (b) The following equations show how we can use the Euclidean algorithm to find the greatest common divisor of 33 and 21. 1 331 x 21 + 12 21 = 1 × 12 +9 12 = 1 x 9 +3 The algorithm shows that gcd (33,21) = 3. Find the integers x and y such that 33x +21y = 3.
Transcribed Image Text:(a) Use the Euclidean algorithm to find the greatest common divisor of 21 and 13. Show all your working. (b) The following equations show how we can use the Euclidean algorithm to find the greatest common divisor of 33 and 21. 1 331 x 21 + 12 21 = 1 × 12 +9 12 = 1 x 9 +3 The algorithm shows that gcd (33,21) = 3. Find the integers x and y such that 33x +21y = 3.
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