Question 71
Find all integers $n \ge 2$ for which there exist $x_1, x_2, \dots, x_n \in \mathbb{R}^*$ such that
$$
x_1 + x_2 + \dots + x_n = \frac{1}{x_1} + \frac{1}{x_2} + \dots + \frac{1}{x_n} = 0.
$$
$$
x_1 + x_2 + \dots + x_n = \frac{1}{x_1} + \frac{1}{x_2} + \dots + \frac{1}{x_n} = 0.
$$