Continuous function of one variable Let $f(x)$ continuous function on $R$ wich can be in different signs. Prove, that there is exists an arithmetic progression $a, b, c   (a<b<c)$,  such that $f(a)+f(b)+f(c)=0$.

HINT:
1) Think about the intermediate value theorem. 
2) Think about some $x$ and some $y$ with $f(x)\gt0$ and $f(y)\lt0$. 
