problem 30

/*Surprisingly there are only three numbers that can be written as the sum of fourth powers of their digits:

1634 = 14 + 64 + 34 + 44
8208 = 84 + 24 + 04 + 84
9474 = 94 + 44 + 74 + 44
As 1 = 14 is not a sum it is not included.

The sum of these numbers is 1634 + 8208 + 9474 = 19316.

Find the sum of all the numbers that can be written as the sum of fifth powers of their digits.
*/

/*

(a + 10b + 100c + 1000d) % a = (a^4 + b^4 + c^4 + d^4) % a

*/

#include <iostream>
#include<string>
#include<math.h>
using namespace std;

int main() {
  int total = 0;
  for(int i = 0; i < 10; i++){
    for(int j = 0; j < 10; j++){
      for(int k = 0; k < 10; k++){
        for(int l = 0; l  < 10; l++){
          for(int n = 0; n < 10; n++){
            for(int m = 0; m < 10; m++){
               int sum_of_pow = pow(i,5) + pow(j,5) + pow(k,5) + pow(l,5) + pow(n,5) + pow(m,5);
               int number  = i * 100000 + j * 10000 + k * 1000 + l * 100 + n * 10  + m;
               if(sum_of_pow == number){
               total += number;
              }
            }
          }
        }
      }
    }
  }
  cout << total - 1 <<endl;
  return 0;
}