1986 IMO 第 4 题

(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 $$x y z=p^{n}(x+y+z)$$ that do not differ only by permutation.

(CZS 3) 设$n$为正整数，$p$为素数，$p>3$。找到至少 $3(n+1)$ [简单版本：$2(n+1)]$ 正整数序列 $x, y, z$ 满足 $$x y z=p^{n}(x+y+z)$$ 且仅因排列而不同。