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🦋 Sum of 2 different squares, 3 different ways

Over at Unfogged, Frederick suggests that 325 is the smallest number which can be expressed as a sum of two perfect squares three different ways. I just wrote a program to check this which confirms Frederick's suspicion; here it is if you want to check my logic.

 #include 
 
 int perfect[] = {
     1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 
     11 * 11, 12 * 12, 13 * 13,
     14 * 14, 15 * 15, 16 * 16, 17 * 17, 
     18 * 18, 19 * 19, 20 * 20
     };
 
 bool IsSumOfSq(int s, int &a, int &b, int x1, int x2)
 {
     for (int i = a + 1; i < 20; ++i)
     {
         if (s < perfect[i])
             return false;
         int diff = s - perfect[i];
         for (int j = 0; j < 20; ++j)
             if (j == x1 || j == x2)
                 continue;
             else if (perfect[j] == diff)
             {
                 a = i;
                 b = j;
                 return true;
             }
     }
 }
 
 int main()
 {
     int i;
     for (i = 0; i < 400; ++i)
     {
         int a = -1, b;
         if (IsSumOfSq(i, a, b, -1, -1))
         {
             int c = a, d;
             if (IsSumOfSq(i, c, d, a, -1))
             {
                 int e = c, f;
                 if (IsSumOfSq(i, e, f, a, c))
                 {
                     printf("%d = %d^2 + %d^2\n"
                           "    = %d^2 + %d^2\n"
                           "    = %d^2 + %d^2", 
                         i, a + 1, b + 1, c + 1, 
                         d + 1, e + 1, f + 1);
                     break;
                 }
             }
         }
     }
     return 0;
 }
 

Output:

325 = 1^2 + 18^2
    = 6^2 + 17^2
    = 10^2 + 15^2

posted evening of Friday, January 13th, 2006
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