Question 38
Determine, with proof, whether or not there exist distinct positive integers $a_{1}, a_{2}, \ldots, a_{n}$ such that
$$
\frac{1}{a_{1}} + \frac{1}{a_{2}} + \cdots + \frac{1}{a_{n}} = 2019.
$$
$$
\frac{1}{a_{1}} + \frac{1}{a_{2}} + \cdots + \frac{1}{a_{n}} = 2019.
$$