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Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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
Transcribed Image Text:The extended Euclidean algorithm computes
the gcd of two integers ro and r₁ as a linear
combination of the inputs.
gcd(ro, r₁) = s.ro + t •rı
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
ri is expressed as a linear combination of the
inputs.
ri = siro + tir₁.
This produces a sequence of numbers
To, T1,
Tn-1, Tn where r = 0 and
gcd(ro, r₁) = Tn-1. Suppose that ro = 420 and
T1 = 382.
Give the sequence ro, T1,..., Tn-1, în in the blank
below. Enter your answer as a comma separated list of
numbers.
What is GCD(420,382)?
What is s?
What is t?
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