About: Quadratic integer

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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 x2 + bx + c = 0 with b and c (usual) integers. When algebraic integers are considered, the usual integers are often called rational integers. Quadratic integers occur in the solutions of many Diophantine equations, such as Pell's equations, and other questions related to integral quadratic forms. The study of rings of quadratic integers is basic for many questions of algebraic number theory.

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rdf:type	Thing
rdfs:label	Entero cuadrático (es) Entier quadratique (fr) 이차 정수 (ko) Quadratic integer (en) Kwadratisch geheel getal (nl)
rdfs:comment	Los enteros cuadráticos, en los predios de la teoría de números, son una generalización de los enteros racionales a los cuerpos cuadráticos. Entre ejemplos importantes, se mencionan los enteros gaussianos y los enteros de Eisenstein. Aunque han sido estudiados, en un lapso mayor de cien años, muchos problemas continúan en ayunos de solución. (es) In de algebraïsche getaltheorie, een deelgebied van de wiskunde, zijn kwadratische gehele getallen een veralgemening van de rationale gehele getallen naar kwadratische velden. Belangrijke voorbeelden zijn de gehele getallen van Gauss en de gehele getallen van Eisenstein. Hoewel kwadratisch gehele getallen al meer dan honderd jaar onderzocht worden, kent dit onderzoeksgebied nog veel niet opgeloste problemen. (nl) 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 x2 + bx + c = 0 with b and c (usual) integers. When algebraic integers are considered, the usual integers are often called rational integers. Quadratic integers occur in the solutions of many Diophantine equations, such as Pell's equations, and other questions related to integral quadratic forms. The study of rings of quadratic integers is basic for many questions of algebraic number theory. (en) En mathématiques, un entier quadratique est un nombre complexe, racine d'un polynôme unitaire du second degré à coefficients entiers. La notion de nombre algébrique de degré inférieur ou égal à 2 est plus générale : elle correspond à un nombre complexe, racine d'un polynôme du second degré à coefficients seulement rationnels. (fr)
rdfs:seeAlso	Euclidean domain
foaf:depiction
dcterms:subject	Integers Ring theory Algebraic number theory
Wikipage page ID	21834785 (xsd:integer)
Wikipage revision ID	1092148245 (xsd:integer)
Link from a Wikipage to another Wikipage	Principal ideal Principal ideal domain Quadratic field Root of unity Principal ideal ring Euclidean function Brahmagupta Pell's equation Peter Gustav Lejeune Dirichlet Richard Dedekind Ring of integers Unit (ring theory) Dedekind domain Integral domain Kurt Heegner Multiplicative inverse Quadratic forms Integers Ring theory Complex number Generalized Riemann hypothesis Class number (number theory) Eisenstein integer Fundamental theorem of arithmetic Gaussian integer Golden ratio Multiplication Completely multiplicative function Fundamental unit (number theory) Half-integer Ideal (ring theory) Ideal class group Penrose tiling Automorphism Irrational number Irreducible element Minimal polynomial (field theory) Absolute value Addition Algebraic integer Algebraic number theory Cyclotomic field Euclidean domain Number theory Unique factorization domain Ring (mathematics) Harold Stark Algebraic number theory Diophantine equation Discriminant Square-free integer Square root Class number problem Indian mathematics Integer Integral closure Rational number Real number Stark–Heegner theorem Imaginary number Rotational symmetry Odd integer Gauss Pierre Fermat Carl Gauss Unique factorization
Link from a Wikipage to an external page	http://gdz.sub.uni-goettingen.de/en/dms/load/toc/%3FPPN=PPN30976923X&DMDID=dmdlog1 http://www.jmilne.org/math/CourseNotes/ANT301.pdf https://oeis.org/A000924 https://oeis.org/A003649
sameAs	Quadratic integer Quadratic integer Quadratic integer Quadratic integer Quadratic integer Quadratic integer Quadratic integer
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