 All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars  perplexus dot info  Zero Sum Expression (Posted on 2015-03-25) Define p ⊗ q = p+q-p*q, and find all possible triplets (a, b, c) of integers such that:
a ⊗ ( b ⊗ c) + b ⊗ (c ⊗ a) + c ⊗ (a ⊗ b) = 0

 No Solution Yet Submitted by K Sengupta No Rating Comments: ( Back to comment list | You must be logged in to post comments.) computer exploration | Comment 1 of 2
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

For ptot = 0 To 10000
For a0 = 0 To ptot / 3
For b0 = a0 To (ptot - a0) / 2
For a = -a0 To a0 Step 2 * a0
For b = -b0 To b0 Step 2 * b0
cd = ptot - a - b
For c = -cd To cd Step 2 * cd
If f(a, f(b, c)) + f(b, f(c, a)) + f(c, f(a, b)) = 0 Then
Text1.Text = Text1.Text & a & Str(b) & Str(c) & crlf
DoEvents
End If: If c = 0 Then Exit For
Next c: If b = 0 Then Exit For
Next: If a = 0 Then Exit For
Next
Next
Next
Next ptot

Text1.Text = Text1.Text & crlf & crlf

End Sub

Function f(x, y)
f = x + y - x * y
End Function

finds only (0,0,0) and (0,2,2), as it shows only ascending absolute values, so permutations of the latter should also work.

 Posted by Charlie on 2015-03-25 15:44:18 Please log in:
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