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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.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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