Question 29
Let $n \geqslant 2018$ be an integer, and let $a_{1}, a_{2}, \ldots, a_{n}, b_{1}, b_{2}, \ldots, b_{n}$ be pairwise distinct positive integers not exceeding $5n$. Suppose that the sequence
$$
\frac{a_{1}}{b_{1}}, \frac{a_{2}}{b_{2}}, \ldots, \frac{a_{n}}{b_{n}}
$$
forms an arithmetic progression. Prove that the terms of the sequence are equal.
$$
\frac{a_{1}}{b_{1}}, \frac{a_{2}}{b_{2}}, \ldots, \frac{a_{n}}{b_{n}}
$$
forms an arithmetic progression. Prove that the terms of the sequence are equal.