Question 43
Find all prime numbers $p$ for which there exist non-negative integers $x$, $y$ and $z$ such that the number
$$
x^p + y^p + z^p - x - y - z
$$
is a product of exactly three distinct prime numbers.
$$
x^p + y^p + z^p - x - y - z
$$
is a product of exactly three distinct prime numbers.