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.


  0:?x0
&   whl
  ' ( 1+!x0:<250:?x0
    & out$(x0 !x0)
    & 0:?x1
    &   whl
      ' ( 1+!x1:~>!x0:?x1
        & out$(x0 !x0 x1 !x1)
        & 0:?x2
        &   whl
          ' ( 1+!x2:~>!x1:?x2
            & 0:?x3
            &   whl
              ' ( 1+!x3:~>!x2:?x3
                &   (!x0^5+!x1^5+!x2^5+!x3^5)^1/5
                  : (   #?y
                      & out$(x0 !x0 x1 !x1 x2 !x2 x3 !x3 y !y)
                      & 250:?x0:?x1:?x2:?x3
                    | ?
                    )
                )
            )
        )
    )