Algebraic integers

Algebraic integers are special numbers that can be roots of polynomial equations with integer coefficients, where the leading coefficient is 1. In simpler terms, they are numbers that fit neatly into certain mathematical structures. Examples include regular integers, rational numbers (like \( \frac{1}{2} \) if you consider \( x - \frac{1}{2} = 0 \)), and some square roots (like \( \sqrt{2} \)), depending on the equation's form. Algebraic integers are fundamental in number theory, helping mathematicians understand properties of numbers and their relationships.