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.


' Euler sum of powers conjecture - 03/07/2015
  'find: x1^5+x2^5+x3^5+x4^5=x5^5
  '-> x1=27 x2=84 x3=110 x4=133 x5=144
  maxn=250
  For i=1 to maxn
	p5[i]=Math.Power(i,5)
  EndFor
  For x1=1 to maxn-4
    For x2=x1+1 to maxn-3
      'TextWindow.WriteLine("x1="+x1+", x2="+x2)
      For x3=x2+1 to maxn-2
        'TextWindow.WriteLine("x1="+x1+", x2="+x2+", x3="+x3)
        For x4=x3+1 to maxn-1
          'TextWindow.WriteLine("x1="+x1+", x2="+x2+", x3="+x3+", x4="+x4)
          x5=x4+1
          valx=p5[x5]
          sumx=p5[x1]+p5[x2]+p5[x3]+p5[x4]
          While x5<=maxn and valx<=sumx
            If valx=sumx Then
              TextWindow.WriteLine("Found!")
              TextWindow.WriteLine("-> "+x1+"^5+"+x2+"^5+"+x3+"^5+"+x4+"^5="+x5+"^5")
              TextWindow.WriteLine("x5^5="+sumx)
              Goto EndPgrm
            EndIf
            x5=x5+1
            valx=p5[x5]
          EndWhile 'x5
        EndFor 'x4
      EndFor 'x3
    EndFor 'x2
  EndFor 'x1
 EndPgrm: 