Question 73
For any natural number $n \ge 3$ find integers $a_1 \lt a_2 \lt \dots \lt a_n$ such that the following equality holds:
$$
\frac{a_1}{a_1} + \frac{a_1}{a_2} + \frac{a_1}{a_3} + \dots + \frac{a_1}{a_n} = \frac{a_2}{a_1} + \frac{a_2}{a_2} + \frac{a_2}{a_3} + \dots + \frac{a_2}{a_n}.
$$
(Bogdan Rublyov)
$$
\frac{a_1}{a_1} + \frac{a_1}{a_2} + \frac{a_1}{a_3} + \dots + \frac{a_1}{a_n} = \frac{a_2}{a_1} + \frac{a_2}{a_2} + \frac{a_2}{a_3} + \dots + \frac{a_2}{a_n}.
$$
(Bogdan Rublyov)