Cyclotomic Polynomial of Prime Index

Theorem
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:
 * $\Phi_p \left({x}\right) \Phi_1 \left({x}\right) = x^p - 1$

Thus from Sum of Geometric Progression:
 * $\Phi_p \left({x}\right) = \dfrac {x^p - 1} {x - 1} = x^{p - 1} + x^{p - 2} + \cdots + x + 1$