MathDB

Functional equation

Source: Benelux Mathematical Olympiad 2017, Problem 1

May 6, 2017

algebrafunctional equationalgebra proposed

Problem Statement

Find all functions

f : \Bbb{Q}_{>0}\to \Bbb{Z}_{>0}

such that

f(xy)\cdot \gcd\left( f(x)f(y), f(\frac{1}{x})f(\frac{1}{y})\right) = xyf(\frac{1}{x})f(\frac{1}{y}),

for all

x, y \in \Bbb{Q}_{>0,}

where

\gcd(a, b)

denotes the greatest common divisor of

a

and

b.

Back to Problems View on AoPS