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V teoriji števil so kvadratna cela števila posploševanje običajnih celih števil na kvadratna polja. Kvadratna cela števila so algebrska cela števila druge stopnje, to so rešitve enačb oblike $x^2 + bx + c = 0$ s celimi števili $b$ in $c$. Preprosta primera kvadratnih celih števil sta kvadratni koren racionalnih števil, kot na primer $sqrt 2$, in kompleksno število $i = sqrt –1$, ki generira Gaussova cela ševila. Vsak element kolobarja kvadratnih celih števil, razen $0$ in obrnljivih elementov, se da razcepiti na praelemente v kolobarju kvadratnih celih števil. Nekateri se dajo razcepiti enolično (do vstavljanja obrnljivih elementov in do vrstnega reda faktorjev), drugi pa ne. 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. |
