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.


Public Declare Function GetTickCount Lib "kernel32.dll" () As Long
Public Sub begin()
    start_int = GetTickCount()
    main
    Debug.Print (GetTickCount() - start_int) / 1000 & " seconds"
End Sub
Private Function pow(x, y) As Variant
    pow = CDec(Application.WorksheetFunction.Power(x, y))
End Function
Private Sub main()
    For x0 = 1 To 250
        For x1 = 1 To x0
            For x2 = 1 To x1
                For x3 = 1 To x2
                    sum = CDec(pow(x0, 5) + pow(x1, 5) + pow(x2, 5) + pow(x3, 5))
                    s1 = Int(pow(sum, 0.2))
                    If sum = pow(s1, 5) Then
                        Debug.Print x0 & "^5 + " & x1 & "^5 + " & x2 & "^5 + " & x3 & "^5 = " & s1
                        Exit Sub
                    End If
                Next x3
            Next x2
        Next x1
    Next x0
End Sub