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 Inverse Square Sum (Posted on 2014-05-28)
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)

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 re: Do i err ?? | Comment 2 of 5 |

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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