Question 170
Find all real numbers $a$ and $b$ so that the equality
$$
\lfloor a x + b y \rfloor + \lfloor b x + a y \rfloor = (a + b) \lfloor x + y \rfloor
$$
is true for all real numbers $x$ and $y$.
$$
\lfloor a x + b y \rfloor + \lfloor b x + a y \rfloor = (a + b) \lfloor x + y \rfloor
$$
is true for all real numbers $x$ and $y$.