 All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars  perplexus dot info  Symmetry helps! (Posted on 2016-10-26) Solve the system of equations below, listing all un-ordered triplets of integers:

x^2 −(y+z+yz)x+ (y+z)yz = 0
y^2 −(z+x+zx)y+ (z+x)zx = 0
z^2 −(x+y+xy)z+ (x+y)xy = 0

 See The Solution Submitted by Ady TZIDON No Rating Comments: ( Back to comment list | You must be logged in to post comments.) computer exploration | Comment 1 of 7
The following program has gotten as far as a total of x+y+z=5656 having found only (1,1,1)

For tot = 3 To 10000
For x = 1 To tot / 3
For y = x To (tot - x) / 2
z = tot - x - y
If x * x - (y + z + y * z) * x + (y + z) * y * z = 0 Then
If y * y - (z + x + z * x) * y + (z + x) * z * x = 0 Then
If z * z - (x + y + x * y) * z + (x + y) * x * y = 0 Then
Text1.Text = Text1.Text & x & Str(y) & Str(z) & crlf
End If
End If
End If
DoEvents
Next
Next
Next

 Posted by Charlie on 2016-10-26 12:08:23 Please log in:

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