Quadratic integers are a special class of algebraic integers that can be expressed in the form $$a + b\sqrt{d}$$, where $$a$$ and $$b$$ are integers, and $$d$$ is a square-free integer. These numbers extend the concept of integers to include solutions to polynomial equations with integer coefficients, specifically those of degree two. They play a critical role in number theory and can help form unique factorization domains.
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