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.


#lang racket
(define MAX 250)
(define pow5 (make-vector MAX))
(for ([i (in-range 1 MAX)])
  (vector-set! pow5 i (expt i 5)))  
(define pow5s (list->set (vector->list pow5)))
(let/ec break
  (for* ([x0 (in-range 1 MAX)]
         [x1 (in-range 1 x0)]
         [x2 (in-range 1 x1)]
         [x3 (in-range 1 x2)])
    (define sum (+ (vector-ref pow5 x0)
                   (vector-ref pow5 x1)
                   (vector-ref pow5 x2)
                   (vector-ref pow5 x3)))
    (when (set-member? pow5s sum)
      (displayln (list x0 x1 x2 x3 (inexact->exact (round (expt sum 1/5)))))
      (break))))