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2016 and Perfect Square Puzzle (Posted on 2016-06-22) Difficulty: 3 of 5
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    
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Solution 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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