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This produces a sequence of numbers ro, r1,... , rn-1, "n where r, = 0 and gcd(ro, r1) = rn-1. Suppose that ro = 689 and r, = 406. Give the sequence ro, r1,... , rn-1, "n in the blank below. Enter your answer as a comma separated list of numbers. What is GCD(689,406)? 1 What is s? What is t?

This produces a sequence of numbers ro, r1,... , rn-1, "n where r, = 0 and gcd(ro, r1) = rn-1. Suppose that ro = 689 and r, = 406. Give the sequence ro, r1,... , rn-1, "n in the blank below. Enter your answer as a comma separated list of numbers. What is GCD(689,406)? 1 What is s? What is t?

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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· The extended Euclidean algorithm computes the gcd of two integers ro and r as a linear combination of the inputs. gcd(ro, r1) =S ro + t · r1 Here s and t are integers known as the Bezout coefficients. They are not unique. The algorithm works like the standard Euclidean algorithm, except that at each stage the current remainder r; is expressed as a linear combination of the inputs. ri = S;ro + t;ľ. This produces a sequence of numbers ro, r1, ..., rp-1, rn where r, = 0 and gcd(ro, r1) = rn-1. Suppose that ro = 689 and rı = 406. Give the sequence ro, r1, ..., rp-1, r, in the blank below. Enter your answer as a comma separated list of numbers. What is GCD(689,406)? 1 What is s? What is t?
Transcribed Image Text:· The extended Euclidean algorithm computes the gcd of two integers ro and r as a linear combination of the inputs. gcd(ro, r1) =S ro + t · r1 Here s and t are integers known as the Bezout coefficients. They are not unique. The algorithm works like the standard Euclidean algorithm, except that at each stage the current remainder r; is expressed as a linear combination of the inputs. ri = S;ro + t;ľ. This produces a sequence of numbers ro, r1, ..., rp-1, rn where r, = 0 and gcd(ro, r1) = rn-1. Suppose that ro = 689 and rı = 406. Give the sequence ro, r1, ..., rp-1, r, in the blank below. Enter your answer as a comma separated list of numbers. What is GCD(689,406)? 1 What is s? What is t?
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