If I add a cosine to shah function, what would be final signal's period?

Question

For example:

Let's say signal $y = \cos(2\pi t) + \sum n \delta(t - n)$.

Is that signal periodic, and if yes, what is its period? I assume that shah function adds up spikes, doesn't it?

Answer 1

HINT:

In distribution we are given

$$y(t)=\cos(2\pi t)+\sum_{n\in\mathbb{Z}}n\delta(t-n)$$

Now, what is $y(t+m \times 1)$, for $m\in \mathbb{Z}$?