I don't know how to solve this problem:

Let $\displaystyle f$ be a continuous real function such that $\displaystyle \{f(x)\} = f(\{x\})$ for each $\displaystyle x$

$\displaystyle (\{x\}$ is the fractional part of number x)

Prove that then $\displaystyle f$ or $\displaystyle f(x)-x$ is a periodic function.

Could you help me?