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 Linear*Quadratic = Square (Posted on 2016-11-12)
Find all integers x such that (1+x)(1+x2) is a perfect square.

Prove that there are no others.

 No Solution Yet Submitted by K Sengupta No Rating

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 computer exploration | Comment 1 of 2
Checking integers from -1,000,000 to 1,000,000 finds only

`x  val sqrt0    1   1-1   0   01    4   27  400  20`

DefDbl A-Z
Dim crlf\$

Form1.Visible = True

Text1.Text = ""
crlf = Chr\$(13) + Chr\$(10)

For x0 = 0 To 1000000
st = 2 * x0: fin = x0
If st = 0 Then st = 1
For x = -x0 To fin Step st
DoEvents
sq = (1 + x) * (1 + x * x)
If sq >= 0 Then
sr = Int(Sqr(sq) + 0.5)
If sr * sr = sq Then
Text1.Text = Text1.Text & x & Str(sq) & Str(sr) & crlf
End If
End If
Next x
Next x0

Text1.Text = Text1.Text & crlf & " done"

End Sub

 Posted by Charlie on 2016-11-12 10:59:45

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