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Expression Quotient Puzzle (Posted on 2015-06-16) Difficulty: 3 of 5
Find all pairs (x,y) of positive integers x and y such that:
x + y + 1 divides 2xy and:
x + y − 1 divides x2 + y2 − 1

No Solution Yet Submitted by K Sengupta    
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re: Some, maybe all | Comment 2 of 3 |
(In reply to Some, maybe all by Jer)

Checking for all x and y whose sum is under 46000, assures there are no sporadic cases among those.  (The total was set to go higher, but met overflow around 46,000).


DefDbl A-Z
Dim crlf$



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

 For tot = 2 To 100000
  For x = 1 To tot / 2
    y = tot - x
    If Abs(x - y) <> 1 Then
    sm = tot + 1: prd = 2 * x * y
    If prd Mod sm = 0 Then
      df = tot - 1: sq = x * x + y * y - 1
      If sq Mod df = 0 Then
        Text1.Text = Text1.Text & x & Str(y) & crlf
        DoEvents
      End If
    End If
    End If
  Next
 Next
 
 Text1.Text = Text1.Text & mxn & crlf & " done"
  
End Sub


  Posted by Charlie on 2015-06-16 12:08:54
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