# Cyclotomic Polynomial/Examples

## Examples of Cyclotomic Polynomials

### First Cyclotomic Polynomial

The first cyclotomic polynomial is:

$\Phi_1 \left({x}\right) = x - 1$

### Cyclotomic Polynomial of Prime Index

Let $p$ be a prime number.

The $p$th cyclotomic polynomial is:

$\Phi_p \left({x}\right) = x^{p-1} + x^{p-2} + \cdots + x + 1$