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Bivariate Quadratic Puzzle (Posted on 2015-06-14) Difficulty: 3 of 5
Find all pairs (x, y) of integers that satisfy this equation:

1 + x2y = x2 + 2xy + 2x + y

No Solution Yet Submitted by K Sengupta    
Rating: 3.0000 (1 votes)

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Solution computer exploration gives probable solution Comment 2 of 2 |
x     y
-1    -1
0     1
1    -1
2    -7
3     7

are found by checking all x from negative one million to positive one million and solving for y in the resulting linear equation in y.

DefDbl A-Z
Dim crlf$



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

For x = -1000000 To 1000000
  y = (x * x + 2 * x - 1) / (x * x - 2 * x - 1)
  yr = Int(y + 0.5)
  If Abs((y - yr) / y) < 0.0000001 Then
    Text1.Text = Text1.Text & x & "    " & Str(y) & crlf
  End If
Next
 
 Text1.Text = Text1.Text & crlf & " done"
  
End Sub


  Posted by Charlie on 2015-06-14 11:28:53
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