""" Extended Euclidean Algorithm. Finds 2 numbers a and b such that it satisfies the equation am + bn = gcd(m, n) (a.k.a Bezout's Identity) """ # @Author: S. Sharma # @Date: 2019-02-25T12:08:53-06:00 # @Email: silentcat@protonmail.com # @Last modified by: PatOnTheBack # @Last modified time: 2019-07-05 import sys def extended_euclidean_algorithm(m, n): """ Extended Euclidean Algorithm. Finds 2 numbers a and b such that it satisfies the equation am + bn = gcd(m, n) (a.k.a Bezout's Identity) """ a = 0 a_prime = 1 b = 1 b_prime = 0 q = 0 r = 0 if m > n: c = m d = n else: c = n d = m while True: q = int(c / d) r = c % d if r == 0: break c = d d = r t = a_prime a_prime = a a = t - q * a t = b_prime b_prime = b b = t - q * b pair = None if m > n: pair = (a, b) else: pair = (b, a) return pair def main(): """Call Extended Euclidean Algorithm.""" if len(sys.argv) < 3: print("2 integer arguments required") exit(1) m = int(sys.argv[1]) n = int(sys.argv[2]) print(extended_euclidean_algorithm(m, n)) if __name__ == "__main__": main()