Hl! I do not understand this exercise

Recall that $\displaystyle \mathbb{R}^\mathbb{R}$ , the set of all real valued funtions of a real variable, is a commutative ring under pointwise addition and multiplication.

Let $\displaystyle n\geq{0}$ be an integer, and let $\displaystyle I_n$ be the set of all functions in $\displaystyle \mathbb{R}^\mathbb{R}$ vanishing on integer multiples of $\displaystyle n$

Find a function that is in $\displaystyle I_8$ but not in $\displaystyle I_4$

I do not understand why $\displaystyle I_n$ is an ideal and I can not find the function

Thanks