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Integral Proof (Posted on 2015-01-26) Difficulty: 3 of 5
Prove that

tan6(pi/9) + tan6(2pi/9) + tan6(4pi/9)

is an integer, and find the value of this integer.

No Solution Yet Submitted by Danish Ahmed Khan    
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Some Thoughts no proof, but the integer is... (spoiler) | Comment 1 of 3
33272.9999999999..., or 33273

from

DefDbl A-Z
Dim crlf$

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

Private Sub Form_Load()
 Text1.Text = ""
 crlf$ = Chr(13) + Chr(10)
 Form1.Visible = True
 DoEvents
 
 pi = Atn(1) * 4
 v = Tan(pi / 9) ^ 6 + Tan(2 * pi / 9) ^ 6 + Tan(4 * pi / 9) ^ 6
 Text1.Text = Text1.Text & v & crlf
 
 Text1.Text = Text1.Text & " done"
 
End Sub


  Posted by Charlie on 2015-01-26 13:24:51
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