Let $x_1, x_2, ... , x_n$ be a real numbers such that 1) $1 \le x_1, x_2, ... , x_n \le 160$ 2) $x^{2}_{i} + x^{2}_{j} + x^{2}_{k} \ge 2(x_ix_j + x_jx_k + x_kx_i)$ for all $1\le i < j < k \le n$ Find the largest possible $n$.
Source: Kazakhstan MO 2020
Tags: algebra, Kazakhstan, inequalities
Let $x_1, x_2, ... , x_n$ be a real numbers such that 1) $1 \le x_1, x_2, ... , x_n \le 160$ 2) $x^{2}_{i} + x^{2}_{j} + x^{2}_{k} \ge 2(x_ix_j + x_jx_k + x_kx_i)$ for all $1\le i < j < k \le n$ Find the largest possible $n$.