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Integers dividing sum of its neighbours.

Source: IMOC 2021 N4

August 11, 2021
number theory

Problem Statement

There are m3m \geq 3 positive integers, not necessarily distinct, that are arranged in a circle so that any positive integer divides the sum of its neighbours. Show that if there is exactly one 11, then for any positive integer nn, there are at most ϕ(n)\phi(n) copies of nn.
Proposed By- (usjl, adapted from 2014 Taiwan TST)