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Natural number divisibility FE

Source: Swiss 2020 Final Round First Exam Problem 1

March 1, 2020
algebranumber theoryDivisibility

Problem Statement

Let N\mathbb N be the set of positive integers. Find all functions f ⁣:N→Nf\colon\mathbb N\to \mathbb N such that for every m,n∈Nm,n\in \mathbb N, f(m)+f(n)∣m+n. f(m)+f(n)\mid m+n.
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