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.


 
(ql:quickload :alexandria)
(let ((fifth-powers (mapcar #'(lambda (x) (expt x 5))
                            (alexandria:iota 250))))
  (loop named outer for x0 from 1 to (length fifth-powers) do
    (loop for x1 from 1 below x0 do
      (loop for x2 from 1 below x1 do
        (loop for x3 from 1 below x2 do
          (let ((x-sum (+ (nth x0 fifth-powers)
                          (nth x1 fifth-powers)
                          (nth x2 fifth-powers)
                          (nth x3 fifth-powers))))
            (if (member x-sum fifth-powers)
                  (return-from outer (list x0 x1 x2 x3 (round (expt x-sum 0.2)))))))))))
 