Question 85
Let $p$ be an odd positive integer. Find all values of the natural numbers $n \ge 2$ for which holds
$$
\sum_{i=1}^{n} \prod_{j \neq i} (x_i - x_j)^p \geq 0,
$$
where $x_1, x_2, \dots, x_n$ are any real numbers.
$$
\sum_{i=1}^{n} \prod_{j \neq i} (x_i - x_j)^p \geq 0,
$$
where $x_1, x_2, \dots, x_n$ are any real numbers.