Question 44
Prove that, for every positive integer $n \ge 2$, there exist positive integers $a_1, a_2, \dots, a_n$ such that for all $1 \le i \lt j \le n$ the expression
$$
\frac{a_j + a_i}{a_j - a_i}
$$
is a positive integer.
$$
\frac{a_j + a_i}{a_j - a_i}
$$
is a positive integer.