About: Quartic reciprocity

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Quartic or biquadratic reciprocity is a collection of theorems in elementary and algebraic number theory that state conditions under which the congruence x4 ≡ p (mod q) is solvable; the word "reciprocity" comes from the form of some of these theorems, in that they relate the solvability of the congruence x4 ≡ p (mod q) to that of x4 ≡ q (mod p).

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rdfs:label	Quartic reciprocity (en) Характер биквадратичного вычета (ru) Kvartisk reciprocitet (sv)
rdfs:comment	Quartic or biquadratic reciprocity is a collection of theorems in elementary and algebraic number theory that state conditions under which the congruence x4 ≡ p (mod q) is solvable; the word "reciprocity" comes from the form of some of these theorems, in that they relate the solvability of the congruence x4 ≡ p (mod q) to that of x4 ≡ q (mod p). (en) Inom matematiken är kvartisk eller bikvadratisk reciprocitet en samling satser om lösbarheten av kongruensen x4 ≡ p (mod q). Ordet "reciprocitet" kommer från det att dessa satser relaterar lösbarheten av kongruensen x4 ≡ p (mod q) till lösbarheten av kongruensen x4 ≡ q (mod p). (sv) Характер биквадратичного вычета — теоретико-числовая функция двух аргументов, являющаяся частным случаем . Также является характером в простом поле. Характер биквадратичного вычета является аналогом символа Лежандра, и для его вычисления используется биквадратичный закон взаимности, являющийся аналогом квадратичного закона взаимности. (ru)
dcterms:subject	Theorems in number theory Modular arithmetic Algebraic number theory
Wikipage page ID	20131133 (xsd:integer)
Wikipage revision ID	986837166 (xsd:integer)
Link from a Wikipage to another Wikipage	Carl Friedrich Gauss Primitive root modulo n Algebraic number field Ring of integers Cubic reciprocity Index of a subgroup Jacobi symbol Theorems in number theory Quadratic residue Gaussian integers Greatest common divisor Congruence relation Leonhard Euler Modular arithmetic Disquisitiones Arithmeticae Algebraic number theory Cyclotomic field Euler's criterion Fermat's little theorem Number theory Legendre symbol Complex conjugation Unique factorization domain Quadratic reciprocity Ring (mathematics) Algebraic number theory Eisenstein reciprocity Eisenstein integers Springer Science+Business Media Group theory Integers Octic reciprocity Rational reciprocity law Artin reciprocity
Link from a Wikipage to an external page	http://www.fen.bilkent.edu.tr/~franz/publ/aar2.pdf https://zenodo.org/record/1709626/files/article.pdf http://matwbn.icm.edu.pl/ksiazki/aa/aa67/aa6747.pdf
sameAs	Quartic reciprocity Quartic reciprocity Quartic reciprocity Quartic reciprocity Quartic reciprocity Quartic reciprocity
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Mathworld dbt:Note dbt:Ref_label dbt:Reflist dbt:Short_description
title	Biquadratic Reciprocity Theorem (en)
urlname	BiquadraticReciprocityTheorem (en)
has abstract	Quartic or biquadratic reciprocity is a collection of theorems in elementary and algebraic number theory that state conditions under which the congruence x4 ≡ p (mod q) is solvable; the word "reciprocity" comes from the form of some of these theorems, in that they relate the solvability of the congruence x4 ≡ p (mod q) to that of x4 ≡ q (mod p). (en) Inom matematiken är kvartisk eller bikvadratisk reciprocitet en samling satser om lösbarheten av kongruensen x4 ≡ p (mod q). Ordet "reciprocitet" kommer från det att dessa satser relaterar lösbarheten av kongruensen x4 ≡ p (mod q) till lösbarheten av kongruensen x4 ≡ q (mod p). (sv) Характер биквадратичного вычета — теоретико-числовая функция двух аргументов, являющаяся частным случаем . Также является характером в простом поле. Характер биквадратичного вычета является аналогом символа Лежандра, и для его вычисления используется биквадратичный закон взаимности, являющийся аналогом квадратичного закона взаимности. (ru)
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foaf:isPrimaryTopicOf	wikipedia-en:Quartic_reciprocity
is Link from a Wikipage to another Wikipage of	Peter Gustav Lejeune Dirichlet Cubic reciprocity Quartic Gauss's lemma (number theory) Gauss sum Gaussian integer Gotthold Eisenstein Reciprocity Power residue symbol Algebraic number theory Biquadratic reciprocity Legendre symbol Quadratic reciprocity Reciprocity theorem Eisenstein reciprocity Octic reciprocity Rational reciprocity law Biquadratic Reciprocity Theorem
is Wikipage redirect of	Biquadratic reciprocity Biquadratic Reciprocity Theorem
is foaf:primaryTopic of	wikipedia-en:Quartic_reciprocity

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