Question 124
Find all functions $f: \mathbb{R} \to \mathbb{R}$ such that
$$
f(\lfloor x \rfloor y) = f(x)\lfloor f(y) \rfloor, \qquad (1)
$$
for all $x, y \in \mathbb{R}$ (where $\lfloor z \rfloor$ is the greatest integer not exceeding $z$).
$$
f(\lfloor x \rfloor y) = f(x)\lfloor f(y) \rfloor, \qquad (1)
$$
for all $x, y \in \mathbb{R}$ (where $\lfloor z \rfloor$ is the greatest integer not exceeding $z$).