I am a bit confused about approaching this problem,
Let $g(x)$ be a function such that $g(x + 1) + g(x − 1) = g(x)$ for every real $x$. Then for what value of p is the relation $g(x + p) = g(x)$ necessarily true for every real $x$?
The four options given are $5,3,2 \text{ and } 6$.Please explain your answer.