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.


use constant MAX => 250;
my @p5 = (0,map { $_**5 } 1 .. MAX-1);
my $s = 0;
my %p5 = map { $_ => $s++ } @p5;
for my $x0 (1..MAX-1) {
  for my $x1 (1..$x0-1) {
    for my $x2 (1..$x1-1) {
      for my $x3 (1..$x2-1) {
        my $sum = $p5[$x0] + $p5[$x1] + $p5[$x2] + $p5[$x3];
        die "$x3 $x2 $x1 $x0 $p5{$sum}\n" if exists $p5{$sum};
      }
    }
  }
}