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.


import Data.List
import Data.List.Ordered
 
main :: IO ()
main = print $ head [(x0,x1,x2,x3,x4) | 
                                        -- choose x0, x1, x2, x3 
                                        -- so that 250 < x3 < x2 < x1 < x0
                                        x3 <- [1..250-1], 
                                        x2 <- [1..x3-1], 
                                        x1 <- [1..x2-1], 
                                        x0 <- [1..x1-1], 
 
                                        let p5Sum = x0^5 + x1^5 + x2^5 + x3^5,
 
                                        -- lazy evaluation of powers of 5
                                        let p5List = [i^5|i <- [1..]], 
 
                                        -- is sum a power of 5 ?
                                        member p5Sum p5List, 
 
                                        -- which power of 5 is sum ?
                                        let Just x4 = elemIndex p5Sum p5List ]