Question 7
A7 (ARM) Let $f$ be a function from the set of real numbers $\mathbb R$ into itself such that for all $x\in\mathbb R$, we have $|f(x)|\le1$ and
$$f\left(x+\frac{13}{42}\right)+f(x)=f\left(x+\frac16\right)+f\left(x+\frac17\right).$$
Prove that $f$ is a periodic function (that is, there exists a nonzero real number $c$ such that $f(x+c)=f(x)$ for all $x\in\mathbb R$).
$$f\left(x+\frac{13}{42}\right)+f(x)=f\left(x+\frac16\right)+f\left(x+\frac17\right).$$
Prove that $f$ is a periodic function (that is, there exists a nonzero real number $c$ such that $f(x+c)=f(x)$ for all $x\in\mathbb R$).