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.


(off P)
(off S)
 
(for I 250
   (idx
      'P
      (list (setq @@ (** I 5)) I)
      T )
   (for (J I (>= 250 J) (inc J))
      (idx
         'S
         (list (+ @@ (** J 5)) (list I J))
         T ) ) )
(println
   (catch 'found
      (for A (idx 'P)
         (for B (idx 'S)
            (T (<= (car A) (car B)))
            (and
               (lup S (- (car A) (car B)))
               (throw 'found
                  (conc
                     (cadr (lup S (car B)))
                     (cadr (lup S (- (car A) (car B))))
                     (cdr (lup P (car A))) ) ) ) ) ) ) )