Correct problem 9 solution

Python/p009.py

@@ -10,6 +10,8 @@
 #
 # Find the product abc.
 
+from math import gcd
+
 from timeit import default_timer
 
 def main():
@@ -23,14 +25,37 @@ def main():
 #   Euclid's formula, until the one where a+b+c=1000 is found.
     while not found:
         for n in range(1, m):
-            a = m * m - n * n
-            b = 2 * m * n
-            c = m * m + n * n
-
-            if a + b + c == 1000:
-                found = 1
+            if found == 1:
                 break
 
+            if gcd(m, n) == 1 and (m % 2 == 0 and n % 2 != 0 or m % 2 != 0 and n % 2 == 0):
+                a = m * m - n * n
+                b = 2 * m * n
+                c = m * m + n * n
+
+                if a + b + c == 1000:
+                    found = 1
+                    break
+
+                i = 2
+
+                while True:
+                    tmpa = a * i
+                    tmpb = b * i
+                    tmpc = c * i
+
+                    if tmpa + tmpb + tmpc == 1000:
+                        a = tmpa
+                        b = tmpb
+                        c = tmpc
+                        found = 1
+                        break
+
+                    if tmpa + tmpb + tmpc > 1000:
+                        break
+
+                    i = i + 1
+
         m = m + 1
 
     end = default_timer()