IMO Shortlist 2018 problem N7


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3. listopada 2019.
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Let n \ge 2018 be an integer, and let a_1, a_2, \dots, a_n, b_1, b_2, \dots, b_n be pairwise distinct positive integers not exceeding 5n. Suppose that the sequence \frac{a_1}{b_1}, \frac{a_2}{b_2}, \dots, \frac{a_n}{b_n}forms an arithmetic progression. Prove that the terms of the sequence are equal.

Izvor: https://www.imo-official.org/problems/IMO2018SL.pdf