Definition

We define the ring of polynomials of order $p$ where $p$ is prime in terms of the Finite Field of Order p, $\mathbb{F}_{p}$ and we denote it as $$\mathbb{F}_{p}[x]$$where elements are of the form $$a_{n}x^{n}+\dots+a_{1}x+a_{0}$$ where each $a_{i}\in\mathbb{F}_{p}$.