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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