Find the unique triple (x,y,z) of positive integers such that and \frac{1}{x} - \frac{1}{xy} - \frac{1}{xyz} = \frac{1}{3}
1/x - 1/(xy) - 1 / (xyz) = 1/3
Let x =1
1 - 1/3 = 1/(y) + 1/(yz)
2/3 = 1/y + 1/(yz)
2/3 = [ z + 1] / [ yz]
2yz = 3z + 3
2yz - 3z = 3
z (2y - 3) = 3
If y = 2 then z = 3
x,y,z = ( 1,2,3)
Check
1/1 - 1/2 - 1/6 = 1/3
+2651 
