find all functions
Source: Romanian District Olympiad 2015, Grade IX, Problem 4
September 25, 2018
functionalgebra
Problem Statement
Find the functions that satisfy the following relation:
\gcd\left( x,f(y)\right)\cdot\text{lcm}\left(f(x), y\right) = \gcd (x,y)\cdot\text{lcm}\left( f(x), f(y)\right) , \forall x,y\in\mathbb{N} .