Add kraitchik algorithm

Author: daedalus

kraitchik.py

@@ -0,0 +1,21 @@
+from gmpy2 import *
+
+def kraitchik(n):
+    x = isqrt(n)
+    while True:
+        k = 1
+        s = x * x - k * n
+        while s >= 0:
+            if is_square(s):
+                y = isqrt(s)
+                z = x + y
+                w = x - y
+                if z % n != 0 and w % n != 0:
+                    return gcd(z,n),gcd(w,n)
+            s = x * x - k * n
+            k += 1
+        x+=1
+
+print(kraitchik(2041))
+print(kraitchik(65537*65539))
+