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 Triangular and Square Settlement (Posted on 2015-10-13)
A is a triangular number and B is a perfect square such that:
A – B = 2015

Find the four smallest values of A+B

 No Solution Yet Submitted by K Sengupta No Rating

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 computer solution | Comment 2 of 7 |
The four smallest values of A + B are 2017, 2407, 2815 and 4465, from:

ordinal
A      B        A+B    tri   sq
2016      1      2017     63    1
2211    196      2407     66   14
2415    400      2815     69   20
3240   1225      4465     80   35
5151   3136      8287    101   56
8256   6241     14497    128   79
10296   8281     18577    143   91
17391  15376     32767    186  124
18915  16900     35815    194  130
32640  30625     63265    255  175
41616  39601     81217    288  199
72771  70756    143527    381  266
139656 137641    277297    528  371
246051 244036    490087    701  494
315615 313600    629215    794  560

DefDbl A-Z
Dim crlf\$

Form1.Visible = True

Text1.Text = ""
crlf = Chr\$(13) + Chr\$(10)

For addend = 1 To 1000
DoEvents
If tri >= 2015 Then
sq = tri - 2015
sr = Int(Sqr(sq) + 0.5)
If sr * sr = sq Then
Text1.Text = Text1.Text & mform(tri, "######0") & mform(sq, "######0") & "   " & mform(tri + sq, "######0") & mform(addend, "######0") & mform(sr, "####0") & crlf
End If
End If
Next

Text1.Text = Text1.Text & crlf & " done"

End Sub

Function mform\$(x, t\$)
a\$ = Format\$(x, t\$)
If Len(a\$) < Len(t\$) Then a\$ = Space\$(Len(t\$) - Len(a\$)) & a\$
mform\$ = a\$
End Function

 Posted by Charlie on 2015-10-13 15:34:15

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