Question 128
Find all positive integers $n \ge 3$ such that
$$
n! \mid \prod_{\substack{p \lt q \le n, \\ p,q \text{ primes}}} (p+q).
$$
That is, $n!$ divides the product $\prod_{p \lt q \le n,\ p,q\ \text{primes}} (p+q)$.
$$
n! \mid \prod_{\substack{p \lt q \le n, \\ p,q \text{ primes}}} (p+q).
$$
That is, $n!$ divides the product $\prod_{p \lt q \le n,\ p,q\ \text{primes}} (p+q)$.