Quadratic integer

A quadratic integer is a type of algebraic integer that is a root of a monic polynomial of degree two with integer coefficients. In simpler terms, a quadratic integer can be expressed in the form \( a + b\sqrt{d} \), where \( a \) and \( b \) are integers, and \( d \) is a square-free integer (i.e., \( d \) is not divisible by the square of any prime).