MathDB

N4

Part of 2021-IMOC

Problems(1)

Integers dividing sum of its neighbours.

Source: IMOC 2021 N4

8/11/2021
There are m≥3m \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)
number theory