How will you answer this periodic function?

Question

Let $f_1(x)$ be a periodic function with period $p_1 = a$ and let $f_2(x)$ be a periodic function with period $p_2 = b$. Show that if $a/b$ is a rational number, then $F(x) = (f_1 + f_2)(x)$ is also periodic. Do this by finding a number $T$ such that $F(x + T) = F(x)$.

Note: by definition, $F(x) = f(x) + g(x)$. The period $T$ will, of course, depend on $a$ and $b$.

Answer 1

Hint: if $a/b=m/n$, with $m$ and $n$ positive integers, then $na=mb$. What can you say about $f_1(x+na)$?