About: Gauss's lemma (number theory)

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Gauss's lemma in number theory gives a condition for an integer to be a quadratic residue. Although it is not useful computationally, it has theoretical significance, being involved in some proofs of quadratic reciprocity. It made its first appearance in Carl Friedrich Gauss's third proof (1808) of quadratic reciprocity and he proved it again in his fifth proof (1818).

Attributes	Values
rdfs:label	Gauss's lemma (number theory) (en)
rdfs:comment	Gauss's lemma in number theory gives a condition for an integer to be a quadratic residue. Although it is not useful computationally, it has theoretical significance, being involved in some proofs of quadratic reciprocity. It made its first appearance in Carl Friedrich Gauss's third proof (1808) of quadratic reciprocity and he proved it again in his fifth proof (1818). (en)
sameAs	Gauss's lemma (number theory) Gauss's lemma (number theory)
dbp:wikiPageUsesTemplate	dbt:! dbt:About dbt:Main_article dbt:Math dbt:Reflist dbt:Rp dbt:Short_description dbt:Mset
Subject	Articles containing proofs Quadratic residue Squares in number theory Modular arithmetic Lemmas in number theory
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Gauss's_lemma_(number_theory)?oldid=1073209914&ns=0
Wikipage page ID	2310978 (xsd:integer)
page length (characters) of wiki page	17218 (xsd:nonNegativeInteger)
Wikipage revision ID	1073209914 (xsd:integer)
Link from a Wikipage to another Wikipage	Number theory Proofs of Fermat's little theorem Proofs of quadratic reciprocity Root of unity Algebraic number field Carl Friedrich Gauss Articles containing proofs Quadratic residue Squares in number theory Modular arithmetic Legendre symbol Quadratic reciprocity Quadratic residue Quartic reciprocity Zolotarev's lemma Cubic reciprocity Trigonometric functions Coprime integers Lemmas in number theory Elliptic function Finite field Gaussian integer Gotthold Eisenstein Ideal norm Transfer (group theory) Euler's criterion Leopold Kronecker Ring of integers
has abstract	Gauss's lemma in number theory gives a condition for an integer to be a quadratic residue. Although it is not useful computationally, it has theoretical significance, being involved in some proofs of quadratic reciprocity. It made its first appearance in Carl Friedrich Gauss's third proof (1808) of quadratic reciprocity and he proved it again in his fifth proof (1818). (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Gauss's_lemma_(number_theory)
is rdfs:seeAlso of	Zolotarev's lemma
is Wikipage redirect of	Gauss lemma (number theory)
is Link from a Wikipage to another Wikipage of	Floor and ceiling functions List of things named after Carl Friedrich Gauss 1808 in Germany 1808 in science Berlekamp–Zassenhaus algorithm Cubic reciprocity List of number theory topics Euclid's lemma Gauss lemma (number theory)
is foaf:primaryTopic of	http://en.wikipedia.org/wiki/Gauss's_lemma_(number_theory)

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