If f (x + 2) - f (x) = 1 holds, is f (x) a periodic function?

If f (x + 2) - f (x) = 1 holds, is f (x) a periodic function?

If f (x + 2) - f (x) = 1, it can't be a periodic function
F (0 + 2) - f (0) = 1, f (2) = 1 + F (0), you can construct a "sequence" to overturn this proposition