There is a conjecture in mathematics that held for over two hundred years before it was disproved by the finding of a counterexample in 1966 by Lander and Parkin.



Euler's (disproved) sum of powers   conjecture

  At least  k  positive  kth  powers are required to sum to a  kth  power,  
  except for the trivial case of one  kth power:  yk = yk 



In 1966,   Leon J. Lander   and   Thomas R. Parkin   used a brute-force search on a   CDC 6600   computer restricting numbers to those less than 250.



Task

Write a program to search for an integer solution for:


  x05 + x15 + x25 + x35 == y5 

Where all     xi's   and    y    are distinct integers between   0   and   250   (exclusive).

Show an answer here.



Related tasks

   Pythagorean quadruples. 
   Pythagorean triples.


using System;
 
namespace EulerSumOfPowers {
    class Program {
        const int MAX_NUMBER = 250;
 
        static void Main(string[] args) {
            bool found = false;
            long[] fifth = new long[MAX_NUMBER];
 
            for (int i = 1; i <= MAX_NUMBER; i++) {
                long i2 = i * i;
                fifth[i - 1] = i2 * i2 * i;
            }
 
            for (int a = 0; a < MAX_NUMBER && !found; a++) {
                for (int b = a; b < MAX_NUMBER && !found; b++) {
                    for (int c = b; c < MAX_NUMBER && !found; c++) {
                        for (int d = c; d < MAX_NUMBER && !found; d++) {
                            long sum = fifth[a] + fifth[b] + fifth[c] + fifth[d];
                            int e = Array.BinarySearch(fifth, sum);
                            found = e >= 0;
                            if (found) {
                                Console.WriteLine("{0}^5 + {1}^5 + {2}^5 + {3}^5 = {4}^5", a + 1, b + 1, c + 1, d + 1, e + 1);
                            }
                        }
                    }
                }
            }
        }
    }
}