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NT Arithmetic Progression

Source: IMO SL 2018 N7

July 17, 2019
number theoryprogressionarithmetic sequenceIMO Shortlist

Problem Statement

Let n≥2018n \ge 2018 be an integer, and let a1,a2,…,an,b1,b2,…,bna_1, a_2, \dots, a_n, b_1, b_2, \dots, b_n be pairwise distinct positive integers not exceeding 5n5n. Suppose that the sequence a1b1,a2b2,…,anbn \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.
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