prove that the gcd of the final values for x and y equals the gcd of original x and y in Euclid’s algorithm. i.e. gcd(x, y) = gcd(y, x % y) T = {d : d|x and d|y} >> common divisors of x and y U = {d : d|y and d|(x % y)} >> common divisors of y and x%y Show that sets T = U

prove that the gcd of the final values for x and y equals the gcd of original x and y in Euclid’s algorithm. i.e. gcd(x, y) = gcd(y, x % y) T = {d : d|x and d|y} >> common divisors of x and y U = {d : d|y and d|(x % y)} >> common divisors of y and x%y Show that sets T = U

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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Question

prove that the gcd of the final values for x and y equals the gcd of original x and y in Euclid’s algorithm.

i.e.

gcd(x, y) = gcd(y, x % y)

T = {d : d|x and d|y} >> common divisors of x and y
U = {d : d|y and d|(x % y)} >> common divisors of y and x%y

Show that sets T = U

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