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Find additional pairs (Posted on 2016-08-08) Difficulty: 3 of 5
The pair of positive integers (4,6) satisfies the equation

(2x+1)*x=y^2

Find at least three additional pairs, both x and y below 10^6.

See The Solution Submitted by Ady TZIDON    
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Solution computer solution | Comment 2 of 5 |
x  y         y^2
4 6          36
144 204     41616
4900 6930     48024900
166464 235416     55420693056
5654884 7997214     63955431761796

DefDbl A-Z
Dim crlf$


Private Sub Form_Load()
 Form1.Visible = True
 
 
 Text1.Text = ""
 crlf = Chr$(13) + Chr$(10)
 
 For x = 1 To 20000000
     lhs = (2 * x + 1) * x
     y = Int(Sqr(lhs) + 0.5)
     If lhs = y * y Then
       Text1.Text = Text1.Text & x & Str(y) & "     " & y * y & crlf
     End If
     DoEvents
 Next
 
 Text1.Text = Text1.Text & crlf & " done"
  
End Sub


  Posted by Charlie on 2016-08-08 22:12:14
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