(In reply to
solution assuming all members of the series are integers by Charlie)
The successive squares used to prove the theorem are not necessarily or even usually all the squares in the sequence. In the example given, m^2=25 leads to n^2=215296, but a computer search finds many intervening squares:
square k square root
144 7 12
484 27 22
841 48 29 where the square = 25+17*k
1521 88 39
2116 123 46
3136 183 56
3969 232 63
5329 312 73
6400 375 80
8100 475 90
... limited to first 10
sq = 25 : diff = 17
Do
sq = sq + diff
sr = Int(Sqr(sq) + 0.5)
k = k + 1
If sr * sr = sq Then
Text1.Text = Text1.Text & Str(sq) & Str(k) & " " & sr & crlf
ct = ct + 1
End If
DoEvents
Loop Until ct = 10
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Posted by Charlie
on 2018-03-28 10:25:33 |
BTW...
