Question 88
Let $p$ be a prime number. Determine all triples $(a, b, c)$ of positive integers such that $a + b + c \lt 2p\sqrt{p}$ and
$$
\frac{1}{a} + \frac{1}{b} + \frac{1}{c} = \frac{1}{p}.
$$
$$
\frac{1}{a} + \frac{1}{b} + \frac{1}{c} = \frac{1}{p}.
$$