 All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars  perplexus dot info  Square after square creates a new square (Posted on 2018-12-05) 49 and 1681 are squares with an even number of digits, where both halves are squares, and no zeroes are used.
List all such numbers below 10^10.

 No Solution Yet Submitted by Ady TZIDON No Rating Comments: ( Back to comment list | You must be logged in to post comments.) computer solution | Comment 1 of 3
`number    sq root  two sq roots`
`49             7      2   31681          41      4   9225625       475     15  252528178961 50281    159 2813132976729 55973    177 2778122515625 90125    285 125`

There are no more  through 14-digit numbers, through which the program checked.

``` For n = 1 To 10000000
n2\$ = LTrim(Str(n * n))
l = Len(n2)
If l Mod 2 = 0 And InStr(n2, "0") = 0 Then
l2 = l / 2
sq1 = Val(Left(n2, l2))
sq2 = Val(Mid(n2, l2 + 1))
sr1 = Int(Sqr(sq1) + 0.5)
If sr1 * sr1 = sq1 Then
sr2 = Int(Sqr(sq2) + 0.5)
If sr2 * sr2 = sq2 Then
Text1.Text = Text1.Text & n2 & Str(n) & "    " & sr1 & Str(sr2) & crlf
End If
End If
End If
DoEvents
Next
```

 Posted by Charlie on 2018-12-05 10:28:31 Please log in:

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