## APMO 2016 #5

Discussion on Asian Pacific Mathematical Olympiad (APMO)
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 $x, y, z$.