# Algebraic Integers

An algebraic integer is a complex number that is the solution to an algebraic equation having leading coefficient 1, meaning that the coefficient of the highest power of $$x$$ is 1. For example the equation $$x^2 = 2$$ has leading coefficient 1, and its solutions, namely the square root of 2, and minus the square root of 2, are algebraic integers. On the other hand, the equation $$2x = 1$$ has leading coefficient 2, and its solution, $$x = 1/2$$, is not an algebraic integer. An algebraic integer that is a rational number must be an ordinary integer.

The entries in a character table are algebraic integers.