Show that for every mapping $\displaystyle g:\mathbb{Z}/p\mathbb{Z}\rightarrow\mathbb{Z}/p\mathbb{Z}$, that there exists a polynomial $\displaystyle f(x)\in\mathbb{Z}/p\mathbb{Z}[x]$ such that $\displaystyle f(a) = g(a) $ for all $\displaystyle a\in\mathbb{Z}/p\mathbb{Z}$

I'm pretty sure Lagrange Interpolation is what is needed here but I'm not sure how to use it.