MathDB

BMO Shortlist 2021 A1

Source: BMO Shortlist 2021

May 8, 2022

algebrafunctional equationBMO Shortlist

Problem Statement

Find all functions

f: \mathbb{R}^{+} \rightarrow \mathbb{R}

and

g: \mathbb{R}^{+} \rightarrow \mathbb{R}

such that

f(x^2 + y^2) = g(xy)

holds for all

x, y \in \mathbb{R}^{+}