MathDB
Fractions in an FE taking positive reals

Source: IMO Shortlist 2018 A5 (proposed by South Korea)

July 17, 2019
functionalgebraIMO Shortlist

Problem Statement

Determine all functions f:(0,∞)→Rf:(0,\infty)\to\mathbb{R} satisfying (x+1x)f(y)=f(xy)+f(yx)\left(x+\frac{1}{x}\right)f(y)=f(xy)+f\left(\frac{y}{x}\right) for all x,y>0x,y>0.
Back to ProblemsView on AoPS