Added extended euclidean algorithm (#720)

* Added extended euclidean algorithm

* Fixed extended euclidean algorithm

Maths/extended_euclidean_algorithm.py

@@ -0,0 +1,51 @@
+# @Author: S. Sharma <silentcat>
+# @Date:   2019-02-25T12:08:53-06:00
+# @Email:  silentcat@protonmail.com
+# @Last modified by:   silentcat
+# @Last modified time: 2019-02-26T07:07:38-06:00
+
+import sys
+
+# Finds 2 numbers a and b such that it satisfies
+# the equation am + bn = gcd(m, n) (a.k.a Bezout's Identity)
+def extended_euclidean_algorithm(m, n):
+    a = 0; aprime = 1; b = 1; bprime = 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 = aprime
+        aprime = a
+        a = t - q*a
+
+        t = bprime
+        bprime = b
+        b = t - q*b
+
+    pair = None
+    if m > n:
+        pair = (a,b)
+    else:
+        pair = (b,a)
+    return pair
+
+def main():
+    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()