Question 116
Let $r \ge 2$ be an integer, and let $m_1, n_1, m_2, n_2, \dots, m_r, n_r$ be $2r$ integers such that
$$
|m_i n_j - m_j n_i| = 1
$$
for all $1 \le i \lt j \le r$. Find the largest possible value of $r$.
$$
|m_i n_j - m_j n_i| = 1
$$
for all $1 \le i \lt j \le r$. Find the largest possible value of $r$.