In number theory, quadratic integers are a generalization of the usual integers to quadratic fields. Quadratic integers are algebraic integers of degree two, that is, solutions of equations of the form $x^2 + bx + c = 0$ with $b$ and $c$ (usual) integers. Common examples of quadratic integers are the square roots of rational integers, such as $\sqrt 2$, and the complex number $i = \sqrt –1$, which generates the Gaussian integers. Every element of a quadratic integer ring, apart from $0$ and units, has a factorization into primes in a quadratic integer ring. For some, the factorization is unique (up to insertion of units and the order of factors), and for the others it is not.
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