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N to N function

Source: Indonesia Mathematics Olympiad 2008 Day 2 Problem 4

August 13, 2008
functionalgebrafunctional equationalgebra proposed

Problem Statement

Find all function f:Nā†’N f: \mathbb{N}\rightarrow\mathbb{N} satisfy f(mn)\plus{}f(m\plus{}n)\equal{}f(m)f(n)\plus{}1 for all natural number n n
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