Quadratic Forms

Quadratic forms are mathematical expressions involving variables raised to the second power, often written in the form \( ax^2 + bxy + cy^2 \). In number theory, they help study the properties of integers, such as representing numbers as sums of squares or other polynomial forms. Each specific quadratic form can be used to explore which numbers can be expressed in that form, revealing deeper connections in number theory, such as solutions to equations and the distribution of prime numbers. They play a crucial role in understanding the structure of numbers and their relationships.