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a circle with n points on it, a positive integer at each point

Source: 2020 Dutch BxMO TST p1

November 23, 2020
combinatorics

Problem Statement

For an integer n≥3n \ge 3 we consider a circle with nn points on it. We place a positive integer at each point, where the numbers are not necessary need to be different. Such placement of numbers is called stable as three numbers next to always have product nn each other. For how many values of nn with 3≤n≤20203 \le n \le 2020 is it possible to place numbers in a stable way?
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