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- Quadratic_reciprocity abstract "In number theory, the law of quadratic reciprocity is a theorem about modular arithmetic that gives conditions for the solvability of quadratic equations modulo prime numbers. There are a number of equivalent statements of the theorem.Although the law can be used to tell whether any quadratic equation modulo a prime number has a solution, it does not provide any help at all for actually finding the solution. (The article on quadratic residues discusses algorithms for this.)The theorem was conjectured by Euler and Legendre and first proven by Gauss. He refers to it as the "fundamental theorem" in the Disquisitiones Arithmeticae and his papers, writingThe fundamental theorem must certainly be regarded as one of the most elegant of its type. (Art. 151)Privately he referred to it as the "golden theorem." He published six proofs, and two more were found in his posthumous papers. There are now over 200 published proofs.The first section of this article gives a special case of quadratic reciprocity that is representative of the general case. The second section gives the formulations of quadratic reciprocity found by Legendre and Gauss.".
- Quadratic_reciprocity wikiPageExternalLink QuadraticReciprocityTheorem.html.
- Quadratic_reciprocity wikiPageExternalLink ProofOfQuadraticReciprocityRule.html.
- Quadratic_reciprocity wikiPageExternalLink schauspiel.html.
- Quadratic_reciprocity wikiPageExternalLink kmath075.htm.
- Quadratic_reciprocity wikiPageExternalLink fchrono.html.
- Quadratic_reciprocity wikiPageID "25272".
- Quadratic_reciprocity wikiPageRevisionID "606703811".
- Quadratic_reciprocity hasPhotoCollection Quadratic_reciprocity.
- Quadratic_reciprocity id "p/q076130".
- Quadratic_reciprocity title "Quadratic reciprocity law".
- Quadratic_reciprocity subject Category:Algebraic_number_theory.
- Quadratic_reciprocity subject Category:Modular_arithmetic.
- Quadratic_reciprocity subject Category:Number_theory.
- Quadratic_reciprocity subject Category:Quadratic_residue.
- Quadratic_reciprocity subject Category:Theorems_in_number_theory.
- Quadratic_reciprocity type Abstraction100002137.
- Quadratic_reciprocity type Communication100033020.
- Quadratic_reciprocity type Message106598915.
- Quadratic_reciprocity type Proposition106750804.
- Quadratic_reciprocity type Statement106722453.
- Quadratic_reciprocity type Theorem106752293.
- Quadratic_reciprocity type TheoremsInNumberTheory.
- Quadratic_reciprocity comment "In number theory, the law of quadratic reciprocity is a theorem about modular arithmetic that gives conditions for the solvability of quadratic equations modulo prime numbers. There are a number of equivalent statements of the theorem.Although the law can be used to tell whether any quadratic equation modulo a prime number has a solution, it does not provide any help at all for actually finding the solution.".
- Quadratic_reciprocity label "Kwadratische reciprociteit".
- Quadratic_reciprocity label "Lei da reciprocidade quadrática".
- Quadratic_reciprocity label "Ley de reciprocidad cuadrática".
- Quadratic_reciprocity label "Loi de réciprocité quadratique".
- Quadratic_reciprocity label "Prawo wzajemności reszt kwadratowych".
- Quadratic_reciprocity label "Quadratic reciprocity".
- Quadratic_reciprocity label "Quadratisches Reziprozitätsgesetz".
- Quadratic_reciprocity label "Reciprocità quadratica".
- Quadratic_reciprocity label "Квадратичный закон взаимности".
- Quadratic_reciprocity label "二次互反律".
- Quadratic_reciprocity label "平方剰余の相互法則".
- Quadratic_reciprocity sameAs Quadratisches_Reziprozitätsgesetz.
- Quadratic_reciprocity sameAs Ley_de_reciprocidad_cuadrática.
- Quadratic_reciprocity sameAs Loi_de_réciprocité_quadratique.
- Quadratic_reciprocity sameAs Reciprocità_quadratica.
- Quadratic_reciprocity sameAs 平方剰余の相互法則.
- Quadratic_reciprocity sameAs 이차상호법칙.
- Quadratic_reciprocity sameAs Kwadratische_reciprociteit.
- Quadratic_reciprocity sameAs Prawo_wzajemności_reszt_kwadratowych.
- Quadratic_reciprocity sameAs Lei_da_reciprocidade_quadrática.
- Quadratic_reciprocity sameAs m.069_z.
- Quadratic_reciprocity sameAs Q472883.
- Quadratic_reciprocity sameAs Q472883.
- Quadratic_reciprocity sameAs Quadratic_reciprocity.
- Quadratic_reciprocity wasDerivedFrom Quadratic_reciprocity?oldid=606703811.
- Quadratic_reciprocity isPrimaryTopicOf Quadratic_reciprocity.