Question 116
A positive integer $n$ are given. Positive numbers $x_0, x_1, \dots, x_n$ such that $x_0 x_1 \dots x_n = 1$. Find all positive $\gamma$ such that inequality
$$
x_0^\gamma + x_1^\gamma + \dots + x_n^\gamma \ge \frac{1}{x_0} + \frac{1}{x_1} + \dots + \frac{1}{x_n}
$$
holds for any set of numbers $x_0, x_1, \dots, x_n$.
$$
x_0^\gamma + x_1^\gamma + \dots + x_n^\gamma \ge \frac{1}{x_0} + \frac{1}{x_1} + \dots + \frac{1}{x_n}
$$
holds for any set of numbers $x_0, x_1, \dots, x_n$.