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.


define range = (1 ..^ 250)
 
var p5 = Hash()
var sum2 = Hash()
 
for i in (range) {
    p5{i**5} = i
    for j in (range) {
        sum2{i**5 + j**5} = [i, j]
    }
}
 
var sk = sum2.keys.map{ Num(_) }.sort
 
for p in (p5.keys.map{ Num(_) }.sort) {
 
    var s = sk.first {|s|
        p > s && sum2.exists(p-s)
    } \\ next
 
    var t = (sum2{s} + sum2{p-s} -> map{|n| "#{n}⁵" }.join(' + '))
    say "#{t} = #{p5{p}}⁵"
    break
}