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Inverse Square Sum (Posted on 2014-05-28) Difficulty: 3 of 5
Determine all possible triplets of nonzero perfect squares (A, B, C) that satisfy this equation:
 1     2     3       2
--- + --- + --- =   ---
 A     B     C       3
Prove that there are no others.

No Solution Yet Submitted by K Sengupta    
Rating: 1.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: Do i err ?? | Comment 2 of 5 |
(In reply to Do i err ?? by Ady TZIDON)

Indeed, 9,9,9 does seem the only solution, as verified by


 For totab = 2 To 10000
  For a = 1 To totab -1
   DoEvents
   b = totab - a
   a2 = a * a: b2 = b * b
   num = 9 * a2 * b2
   den = -(6 * a2 + 3 * b2 - 2 * a2 * b2)
   If den > 0 Then
    c2 = num / den
    If c2 = Int(c2) And c2 > 0 Then
      c = Int(Sqr(c2) + 0.5)
      If c * c = c2 Then
        Text1.Text = Text1.Text & Str(a2) & Str(b2) & Str(c2) & crlf
      End If
    End If
   End If
  Next
 Next

for sqrt(a) + sqrt(b) having values all the way up to ten thousand.

  Posted by Charlie on 2014-05-28 13:34:18
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