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Year and Perfect Square Puzzle (Posted on 2015-08-22) Difficulty: 3 of 5
Find all possible pairs (A,B) of positive integers such that:
A2 + B = 2016 and, A + B is a perfect square.

*** As an extra challenge, solve this puzzle without using a computer program aided method.

No Solution Yet Submitted by K Sengupta    
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Solution computer solution | Comment 1 of 2
A = 32, B = 992; A^2 = 1024, A + B = 1024

 For b = 1 To 2015
  a2 = 2016 - b
  a = Int(Sqr(a2) + 0.5)
  If a * a = a2 Then
    tot = a + b
    sr = Int(Sqr(tot) + 0.5)
    If sr * sr = tot Then
      Text1.Text = Text1.Text & a & Str(b) & "     " & a2 & Str(tot) & crlf
    End If
  End If
 Next


  Posted by Charlie on 2015-08-22 15:55:34
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