, 2023

For real number $r$ let $f(r)$ denote the integer that is the closest to $r$ (if the fractional part of $r$ is 1/2, let $f(r)$ be $r-1/2$). Let $a>b>c$ rational numbers such that for all integers $n$ the following is true: $f(na)+f(nb)+f(nc)=n$. What can be the values of $a$, $b$ and $c$?