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.


constant MAX = 250;
 
my %po5{Int};
my %sum2{Int};
 
(1..MAX).map: -> $i {
    %po5{$i**5} = $i;
    for 1..MAX -> $j {
        %sum2{$i**5 + $j**5} = ($i, $j);
    }
}
 
my @sk = %sum2.keys.sort;
%po5.keys.sort.race.map: -> $p {
    for @sk -> $s {
        next if $p <= $s;
        if %sum2{$p - $s} {
            say ((sort |%sum2{$s}[],|%sum2{$p-$s}[]) X~ '⁵').join(' + ') ~ " =  %po5{$p}" ~ "⁵";
            exit;
        }
    }
}