MathDB

3

Part of 2015 Mexico National Olympiad

Problems(1)

functional equation

Source: Mexican Math Olympiad 2015 Problem 3

11/23/2015
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
functionalgebrafunctional equation