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.


 
# Project : Euler's sum of powers conjecture
 
max=250
for w = 1 to max
     for x = 1 to w
          for y = 1 to x
               for z = 1 to y
                    sum = pow(w,5) + pow(x,5) + pow(y,5) + pow(z,5)
                    s1  = floor(pow(sum,0.2))
                    if sum = pow(s1,5) 
                       see "" + w + "^5 + " + x + "^5 + " + y + "^5 + " + z + "^5 = " + s1 + "^5" 
                    ok
               next 
          next
     next 
next 
 