Question 5
Determine all integers $n \geq 2$ such that the polynomial
$$ P(x,y,z)=x^{n}+y^{n}+z^{n}-x^{n-2}y z-x y^{n-2}z-x y z^{n-2} $$
can be written as $P(x,y,z) = Q(x,y,z)R(x,y,z)$, where $Q(x,y,z)$ and $R(x,y,z)$ are nonconstant polynomials with integer coefficients.
$$ P(x,y,z)=x^{n}+y^{n}+z^{n}-x^{n-2}y z-x y^{n-2}z-x y z^{n-2} $$
can be written as $P(x,y,z) = Q(x,y,z)R(x,y,z)$, where $Q(x,y,z)$ and $R(x,y,z)$ are nonconstant polynomials with integer coefficients.