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product of each pair of 2 non-adjacent numbers is divisible by 2015x2016

Source: 2016 Saudi Arabia IMO TST , level 4, III p3

July 29, 2020
combinatoricsnumber theorydivisible

Problem Statement

Let n≥4n \ge 4 be a positive integer and there exist nn positive integers that are arranged on a circle such that: ∙\bullet The product of each pair of two non-adjacent numbers is divisible by 2015⋅20162015 \cdot 2016. ∙\bullet The product of each pair of two adjacent numbers is not divisible by 2015⋅20162015 \cdot 2016. Find the maximum value of nn
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