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CPSC 233 (11)
Tony Tang (9)
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# Math271Quiz2Solutions.pdf

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School
University of Calgary
Department
Computer Science
Course
CPSC 233
Professor
Tony Tang
Semester
Winter

Description
1 MATHEMATICS 271 L02 WINTER 2014 QUIZ 2 Thursday, February 13, 2014 Duration: 30 minutes STUDENT ID# [5] 1. Use the Euclidean Algorithm to ▯nd gcd(685;211) and ▯nd integers x and y so that gcd(685;211) = 685x + 211y. Solution: Using the Euclidean Algorithm, we have 685 = 211(3) + 52 (1) 211 = 52(4) + 3 (2) 52 = 3(17) + 1 (3) 3 = 1(3) + 0 so that gcd(685;211) = 1. To ▯nd x and y satisfying gcd(685;211) = 685x + 211y, gcd(685;211) = 1 = 52(1) ▯ 3(17) by (3) ▯ ▯ = 52(1) ▯ 211(1) ▯ 52(4) (17) by (2) = 52(1) ▯ 211(17) + 52(68) = 52(69) ▯ 211(17) ▯ ▯ = 685(1) ▯ 211(3) (69) ▯ 211(17) by (1) = 685(69) ▯ 211(207) ▯ 211(17) = 685(69) ▯ 211(224) = 685(69) + 221(▯224) so x = 69 and y = ▯224. Alternatively, we may use the \Table Method": 685 211 685 1 0 211 0 1 52 1 ▯3 R ▯ 1R 2 by (1) 3 ▯4 13 R ▯24R 3 by (2)
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