Cyclotomic Polynomial of Prime Index

Example of Cyclotomic Polynomial
Let $p$ be a prime number.

The $p$th cyclotomic polynomial is:
 * $\Phi_p \left({x}\right) = x^{p-1} + x^{p-2} + \cdots + x + 1$

Proof
From Product of Cyclotomic Polynomials, $\Phi_p(x)\Phi_1(x)=x^p-1$. Thus
 * $\Phi_p(x)=\frac{x^p-1}{x-1}= x^{p-1} + x^{p-2} + \cdots + x + 1$