MathNet 2018-part-07 — 177 problems (EN–VI) Question 176

Find all real $a$ for which there exists a function $f: \mathbb{R} \rightarrow \mathbb{R}$ such that $f(x-f(y))=f(x)+a[y]$ for every real $x$ and $y$ ( $[y]$ denotes the integral part of $y$ ).