Let $f$ and $g$ be two periodic functions over $\Bbb{R}$ with the following property: If $T$ is a period of $f$, and $S$ is a period of $g$, then $T/S$ is irrational. 

**Conjecture**: $f+g$ is *not* periodic.

Could you give a proof or a counter example? It is easier if we assume continuity. But is it true for arbitrary real valued functions?