Question 35
Nonzero real numbers $x_1, x_2, \dots, x_n$ satisfy the following conditions:
$$
x_1 - \frac{1}{x_2} = x_2 - \frac{1}{x_3} = \dots = x_{n-1} - \frac{1}{x_n} = x_n - \frac{1}{x_1}.
$$
For which $n$ do the numbers $x_1, x_2, \dots, x_n$ all have to be equal?
$$
x_1 - \frac{1}{x_2} = x_2 - \frac{1}{x_3} = \dots = x_{n-1} - \frac{1}{x_n} = x_n - \frac{1}{x_1}.
$$
For which $n$ do the numbers $x_1, x_2, \dots, x_n$ all have to be equal?