Cyclotomic Integer

A number of the form

$$a_0+a_1\zeta+\ldots+a_{p-1}\zeta^{p-1},$$

where

$$\zeta\equiv e^{2\pi i/p}$$

is a de Moivre Number and $p$ is a Prime number. Unique factorizations of cyclotomic Integers fail for $p>23$.