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Nice integer FE

Source: 2020 Caucasus Mathematical Olympiad Seniors Problem 4

March 16, 2020
functional equationalgebranumber theory

Problem Statement

Find all functions f:N→Nf : \mathbb{N}\rightarrow{\mathbb{N}} such that for all positive integers mm and nn the number f(m)+n−mf(m)+n-m is divisible by f(n)f(n).
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