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.


eulerSumOfPowers: function [top][
    p5: map 0..top => [& ^ 5]
 
    loop 4..top 'a [
        loop 3..a-1 'b [
            loop 2..b-1 'c [
                loop 1..c-1 'd [
                    s: (get p5 a) + (get p5 b) + (get p5 c) + (get p5 d)
                    if integer? index p5 s ->
                        return ~"|a|^5 + |b|^5 + |c|^5 + |d|^5 = |index p5 s|^5"
                ]
            ]
        ]
    ]
 
    return "not found" ; shouldn't reach here
]
 
print eulerSumOfPowers 249