Create euler.py

Author: daedalus

euler.py

@@ -0,0 +1,34 @@
+# /usr/bin/env python
+# code taken from https://maths.dk/teaching/courses/math357-spring2016/projects/factorization.pdf
+
+from gmpy2 import gcd, isqrt
+
+def euler(self, n):
+        if n % 2 == 0:
+            return (n / 2, 2) if n > 2 else (2, 1)
+        end = isqrt(n)
+        a = 0
+        solutionsFound = []
+        firstb = -1
+        while a < end and len(solutionsFound) < 2:
+            bsquare = n - a ** 2
+            if bsquare > 0:
+                b = isqrt(bsquare)
+                if (b ** 2 == bsquare) and (a != firstb) and (b != firstb):
+                    firstb = b
+                    solutionsFound.append([int(b), a])
+            a += 1
+        if len(solutionsFound) < 2:
+            return -1
+        a = solutionsFound[0][0]
+        b = solutionsFound[0][1]
+        c = solutionsFound[1][0]
+        d = solutionsFound[1][1]
+        k = gcd(a - c, d - b)
+        h = gcd(a + c, d + b)
+        m = gcd(a + c, d - b)
+        l = gcd(a - c, d + b)
+        n = (k ** 2 + h ** 2) * (l ** 2 + m ** 2)
+        return [int(k ** 2 + h ** 2) // 2, int(l ** 2 + m ** 2) // 2]
+        
+print(euler(int(sys.argv[1])))