Let $x^3 + y^3 = z!$, where $z > 12$.
1) Prove that the largest prime less than $z$ does not divide x.
2) Prove that $x + y$ is a multiple of $330$.
I noticed that since
$$z > 12,$$
$x$ and $y$ have the same parity.
Then $x^3 + y^3$ could be factored as
$$(x+y)(x^2 - xy + y^2),$$
where both factors had to be either even or odd. Here is where I got stuck.
Any insights on this problem? Any help is appreciated!