First Cyclotomic Polynomial

Example of Cyclotomic Polynomial
The first cyclotomic polynomial is $\Phi_1(x)=x-1$.

Proof
By definition,
 * $\displaystyle \Phi_1 \left({x}\right) = \prod_\zeta \left({x - \zeta}\right)$

where the product runs over all primitive complex first roots of unity. A root of unity has order $1$ iff it equals $1$, so the only factor is $x-1$.