If $g(x+1)+g(x-1)=g(x)$ for all real $x$, then for what $p$ is $g(x+p)=g(x)$ necessarily true?
If $f(x + 1) + f(x − 1) = f(x), \forall x \in \mathbb{R}$,then how to find $k$ such that $f(x + k) = f(x)$?