Question 65
Find all positive integers $n$ for which there exists a positive real number $C$ such that
$$
\sum_{1 \le i \lt j \le n} x_i x_j \le C (x_1 x_2 + \dots + x_{n-1} x_n + x_n x_1)
$$
for all positive real numbers $x_1, \dots, x_n$.
$$
\sum_{1 \le i \lt j \le n} x_i x_j \le C (x_1 x_2 + \dots + x_{n-1} x_n + x_n x_1)
$$
for all positive real numbers $x_1, \dots, x_n$.