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functional equation

Source: Mexican Math Olympiad 2015 Problem 3

November 23, 2015
functionalgebrafunctional equation

Problem Statement

Let N={1,2,3,...}\mathbb{N} =\{1, 2, 3, ...\} be the set of positive integers. Let f:Nā†’Nf : \mathbb{N} \rightarrow \mathbb{N} be a function that gives a positive integer value, to every positive integer. Suppose that ff satisfies the following conditions:
f(1)=1f(1)=1 f(a+b+ab)=a+b+f(ab)f(a+b+ab)=a+b+f(ab)
Find the value of f(2015)f(2015)
Proposed by Jose Antonio Gomez Ortega
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