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.


USING: arrays backtrack kernel literals math.functions
math.ranges prettyprint sequences ;
 
CONSTANT: pow5 $[ 0 250 [a,b) [ 5 ^ ] map ]
 
: xn ( n1 -- n2 n2 ) [1,b) amb-lazy dup ;
 
250 xn xn xn xn drop 4array dup pow5 nths sum dup pow5
member? [ pow5 index suffix . ] [ 2drop fail ] if