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 2016 and Perfect Square Puzzle (Posted on 2016-06-22)
Determine all possible positive integer solutions to this system of equations:
A+B = 2016, and:
A2+B is a perfect square

 No Solution Yet Submitted by K Sengupta No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
 computer solution | Comment 1 of 4
DefDbl A-Z
Dim crlf\$

Private Sub Form_Load()
Form1.Visible = True

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

For a = 1 To 2015
b = 2016 - a
tst = a * a + b
sr = Int(Sqr(tst) + 0.5)
If sr * sr = tst Then
Text1.Text = Text1.Text & a & Str(b) & "     " & tst & Str(sr) & crlf
End If
Next

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

End Sub

finds

181 1835     34596 186

meaning a=181, b=1835 and a^2+b=34596, whose square root is 186.

It could have been done with the table function of a graphing calculator tabulating sqrt(x^2 + (2016-x)), a section of which is:

176                    181.151869987588
177                    182.1208390053154
178                    183.0901417335188
179                    184.0597729000012
180                    185.0297273413113
181                    186
182                    186.9705859219573
183                    187.941480253828
184                    188.9126782405035
185                    189.8841752226867

or a spreadsheet could work as well.

 Posted by Charlie on 2016-06-22 16:15:15
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