Diophantine equation, 3 variables How do I solve the following equation, where $x,y,z$ have to be positive integers?
$$ \frac{x^2}{y} + \frac{y^2}{z}+ \frac{z^2}{x}= \frac{y^2}{x} + \frac{z^2}{y} + \frac{x^2}{z} $$
Given that $$xyz=2205$$

Multiply both sides of the first equation by $xyz$ and try to factor it to linear expressions, you will get$$(x-y)(x-z)(y-z)(x+y+z)=0$$And notice that $2205=3^2 \times 5 \times 7^2$, so exactly two of the three variables are equal.
