Question 4
(CZS 3) Let $n$ be a positive integer and let $p$ be a prime number, $p>3$. Find at least $3(n+1)$ [easier version: $2(n+1)$] sequences of positive integers $x,y,z$ satisfying
$$xyz=p^n(x+y+z)$$
that do not differ only by permutation.
$$xyz=p^n(x+y+z)$$
that do not differ only by permutation.