Question 6
If $x,y$ and $z$ are three consecutive positive integers such that
$$\frac{x}{y}+\frac{y}{z}+\frac{z}{x}+\frac{y}{x}+\frac{x}{z}+\frac{z}{y}$$
is an integer, what is the value of $x+y+z$?
$$\frac{x}{y}+\frac{y}{z}+\frac{z}{x}+\frac{y}{x}+\frac{x}{z}+\frac{z}{y}$$
is an integer, what is the value of $x+y+z$?