Question 37
Show that for every integer $n \ge 3$ there exist positive integers $x_1, x_2, \dots, x_n$, pairwise different, so that $\{2, n\} \subset \{x_1, x_2, \dots, x_n\}$ and
$$
\frac{1}{x_1} + \frac{1}{x_2} + \dots + \frac{1}{x_n} = 1.
$$
$$
\frac{1}{x_1} + \frac{1}{x_2} + \dots + \frac{1}{x_n} = 1.
$$