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Greatest GCD (Posted on 2014-10-12) Difficulty: 3 of 5
The sequence {S(n)} is defined by the relationship: S(n) = 100 + n2, whenever n is a positive integer.

If G(n) = gcd(S(n), S(n+1)), then find the maximum value of G(n).

No Solution Yet Submitted by K Sengupta    
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Some Thoughts computer exploration | Comment 1 of 5
DefDbl A-Z
Dim crlf$


Private Sub Form_Load()
 ChDir "C:\Program Files (x86)\DevStudio\VB\projects\flooble"
 Text1.Text = ""
 crlf$ = Chr(13) + Chr(10)
 Form1.Visible = True
 
 DoEvents
 
 For n = 1 To 100000
  If gcd(s(n), s(n + 1)) > 1 Then
   Text1.Text = Text1.Text & n & Str(s(n)) & Str(s(n + 1)) & "    " & Str(gcd(s(n), s(n + 1))) & crlf
   DoEvents
  End If
 Next




 Text1.Text = Text1.Text & crlf & maxlvl & Str(uct) & " done"
End Sub

Function s(n)
 s = 100 + n * n
End Function

Function gcd(a, b)
  x = a: y = b
  Do
   q = Int(x / y)
   z = x - q * y
   x = y: y = z
  Loop Until z = 0
  gcd = x
End Function

finds the only GCD > 1 is 401 as in:

n    S(n)    S(n+1)      GCD
200  40100   40501       401
601  361301  362504      401
1002 1004104 1006109     401
1403 1968509 1971316     401
1804 3254516 3258125     401
2205 4862125 4866536     401
2606 6791336 6796549     401
3007 9042149 9048164     401
...
95237 9070086269 9070276744     401
95638 9146627144 9146818421     401
96039 9223489621 9223681700     401
96440 9300673700 9300866581     401
96841 9378179381 9378373064     401
97242 9456006664 9456201149     401
97643 9534155549 9534350836     401
98044 9612626036 9612822125     401
98445 9691418125 9691615016     401
98846 9770531816 9770729509     401
99247 9849967109 9850165604     401
99648 9929724004 9929923301     401

  Posted by Charlie on 2014-10-12 14:17:06
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