I’ve been set this problem by my teacher, and had no idea where to start. I have a [Diophantine equation](https://en.wikipedia.org/wiki/Diophantine_equation):

$$
\frac{x^2+y^2+z^2}{x+y+z}=2n
$$

$x, y, z$ and $n$ must be distinct positive integers. I’ve found solutions where there is an equality for any of $x, y$ and $z$ but I haven’t been able to for distinct positive integers, and would appreciate help.