From 2cdbca922ad97e2bee84e2c78343defd221d5b59 Mon Sep 17 00:00:00 2001
From: Daniele Fucini <dfucini@gmail.com>
Date: Sun, 29 Sep 2019 18:03:11 +0200
Subject: [PATCH] Correct problem 9 solution

---
 C/p009.c       | 42 +++++++++++++++++++++++++++++++++---------
 Python/p009.py | 37 +++++++++++++++++++++++++++++++------
 2 files changed, 64 insertions(+), 15 deletions(-)

diff --git a/C/p009.c b/C/p009.c
index c086eae..d0ff0d1 100644
--- a/C/p009.c
+++ b/C/p009.c
@@ -11,10 +11,11 @@
 #include <stdio.h>
 #include <stdlib.h>
 #include <time.h>
+#include "projecteuler.h"
 
 int main(int argc, char **argv)
 {
-   int a, b, c, m, n, found = 0;
+   int a, b, c, tmpa, tmpb, tmpc, i, m, n, found = 0;
    double elapsed;
    struct timespec start, end;
 
@@ -24,16 +25,39 @@ int main(int argc, char **argv)
     * Euclid's formula, until the one where a+b+c=1000 is found.*/
    for(m = 2; found == 0; m++)
    {
-      for(n = 1; n < m; n++)
+      for(n = 1; n < m && !found; n++)
       {
-         a = m * m - n * n;
-         b = 2 * m * n;
-         c = m * m + n * n;
-
-         if(a + b + c == 1000)
+         if(gcd(m, n) == 1 && (m % 2 == 0 && n % 2 != 0 || m % 2 != 0 && n % 2 == 0))
          {
-            found = 1;
-            break;
+            a = m * m - n * n;
+            b = 2 * m * n;
+            c = m * m + n * n;
+
+            if(a + b + c == 1000)
+            {
+               found = 1;
+               break;
+            }
+
+            i = 2;
+
+            do
+            {
+               tmpa = a * i;
+               tmpb = b * i;
+               tmpc = c * i;
+
+               if(tmpa + tmpb + tmpc == 1000)
+               {
+                  a = tmpa;
+                  b = tmpb;
+                  c = tmpc;
+                  found = 1;
+                  break;
+               }
+               
+               i++;
+            }while(tmpa + tmpb + tmpc < 1000);
          }
       }
    }
diff --git a/Python/p009.py b/Python/p009.py
index 64125c9..2dbb14c 100644
--- a/Python/p009.py
+++ b/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()