# algebraic integer

## English

### Etymology

The idea of integer here is that the coefficient of the highest power ${\displaystyle x^{n}}$ term is 1.

### Noun

algebraic integer ‎(plural algebraic integers)

1. (mathematics) A number (real or complex) which is a root of a monic polynomial whose coefficients are integers.
A Gaussian integer ${\displaystyle z=a+ib}$ is an algebraic integer since it is a solution of either the equation ${\displaystyle z^{2}+(-2a)z+(a^{2}+b^{2})=0}$ or the equation ${\displaystyle z-a=0}$.