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f(x)+f(y)|x^2-y^2 over N

Source: IMOC 2017 N5

August 14, 2021
number theoryfefunctional equation

Problem Statement

Find all functions f:N→Nf:\mathbb N\to\mathbb N such that f(x)+f(y)∣x2−y2f(x)+f(y)\mid x^2-y^2holds for all x,y∈Nx,y\in\mathbb N.
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