APMO 2016 #5
Posted: Fri Aug 05, 2016 10:17 am
Find all functions $f: \mathbb{R}^+ \to \mathbb{R}^+$ such that
$$(z + 1)f(x + y) = f(xf(z) + y) + f(yf(z) + x),$$for all positive real numbers $x, y, z$.
$$(z + 1)f(x + y) = f(xf(z) + y) + f(yf(z) + x),$$for all positive real numbers $x, y, z$.