Question 84
Find all positive integers $n$ for which there exist $n$ distinct positive integers $a_1, a_2, \dots, a_n$, none of them greater than $n^2$, such that
$$
\frac{1}{a_1} + \frac{1}{a_2} + \dots + \frac{1}{a_n} = 1.
$$
$$
\frac{1}{a_1} + \frac{1}{a_2} + \dots + \frac{1}{a_n} = 1.
$$