Find all possible positive integer solutions to this equation:

A^N - B^N = 2015, whenever N ≥ 2

Note: The common exponent must also be an integer.

a      b  n
48    17 2
84    71 2
204  199 2
1008 1007 2
14     9 3

from

DefDbl A-Z
Dim crlf$



Private Sub Form_Load()
 Form1.Visible = True
 
 Text1.Text = ""
 crlf = Chr$(13) + Chr$(10)

 For n = 2 To 11
   tot = 3
   Do
    'Text1.Text = Text1.Text & tot & crlf
    DoEvents
    noSoln = 0
    soln = 0
    For b = Int(tot / 2) To 1 Step -1
     a = tot - b
     aton = Int(a ^ n + 0.5)
     bton = Int(b ^ n + 0.5)
     If aton > maxnum Then maxnum = aton
     If bton > maxnum Then maxnum = bton
     diff = aton - bton
     If diff > 2015 And a - b = 1 Then noSoln = 1: Exit For
     If diff > 2015 Then Exit For
     If diff = 2015 Then
       Text1.Text = Text1.Text & a & Str(b) & Str(n) & crlf
       Exit For
     End If
    Next
    tot = tot + 1
   Loop Until noSoln
 Next

 
 Text1.Text = Text1.Text & crlf & maxnum & " done"
  
End Sub

Posted by Charlie on 2015-06-30 16:19:44