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Symmetry helps! (Posted on 2016-10-26) Difficulty: 4 of 5
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    
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Some Thoughts 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
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