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- Zolotarev's_lemma abstract "In number theory, Zolotarev's lemma states that the Legendre symbolfor an integer a modulo an odd prime number p, where p does not divide a, can be computed as the sign of a permutation:where ε denotes the signature of a permutation and πa is the permutation of the nonzero residue classes mod p induced by multiplication by a. For example, take a = 2 and p = 7. The nonzero squares mod 7 are 1, 2, and 4, so (2|7) = 1 and (6|7) = −1. Multiplication by 2 on the nonzero numbers mod 7 has the cycle decomposition (1,2,4)(3,6,5), so the sign of this permutation is 1, which is (2|7). Multiplication by 6 on the nonzero numbers mod 7 has cycle decomposition (1,6)(2,5)(3,4), whose sign is −1, which is (6|7).".
- Zolotarev's_lemma wikiPageExternalLink ?op=getobj&from=objects&id=4043.
- Zolotarev's_lemma wikiPageID "2995566".
- Zolotarev's_lemma wikiPageRevisionID "544172149".
- Zolotarev's_lemma hasPhotoCollection Zolotarev's_lemma.
- Zolotarev's_lemma subject Category:Articles_containing_proofs.
- Zolotarev's_lemma subject Category:Lemmas.
- Zolotarev's_lemma subject Category:Number_theory.
- Zolotarev's_lemma subject Category:Permutations.
- Zolotarev's_lemma subject Category:Quadratic_residue.
- Zolotarev's_lemma type Abstraction100002137.
- Zolotarev's_lemma type Change107296428.
- Zolotarev's_lemma type Communication100033020.
- Zolotarev's_lemma type Event100029378.
- Zolotarev's_lemma type Happening107283608.
- Zolotarev's_lemma type Lemma106751833.
- Zolotarev's_lemma type Lemmas.
- Zolotarev's_lemma type Message106598915.
- Zolotarev's_lemma type Permutations.
- Zolotarev's_lemma type Proposition106750804.
- Zolotarev's_lemma type PsychologicalFeature100023100.
- Zolotarev's_lemma type Statement106722453.
- Zolotarev's_lemma type Substitution107443761.
- Zolotarev's_lemma type Variation107337390.
- Zolotarev's_lemma type YagoPermanentlyLocatedEntity.
- Zolotarev's_lemma comment "In number theory, Zolotarev's lemma states that the Legendre symbolfor an integer a modulo an odd prime number p, where p does not divide a, can be computed as the sign of a permutation:where ε denotes the signature of a permutation and πa is the permutation of the nonzero residue classes mod p induced by multiplication by a. For example, take a = 2 and p = 7. The nonzero squares mod 7 are 1, 2, and 4, so (2|7) = 1 and (6|7) = −1.".
- Zolotarev's_lemma label "Lemme de Zolotarev".
- Zolotarev's_lemma label "Zolotarev's lemma".
- Zolotarev's_lemma label "Лемма Золотарёва".
- Zolotarev's_lemma sameAs Lemme_de_Zolotarev.
- Zolotarev's_lemma sameAs m.08jgl4.
- Zolotarev's_lemma sameAs Q3229349.
- Zolotarev's_lemma sameAs Q3229349.
- Zolotarev's_lemma sameAs Zolotarev's_lemma.
- Zolotarev's_lemma wasDerivedFrom Zolotarev's_lemma?oldid=544172149.
- Zolotarev's_lemma isPrimaryTopicOf Zolotarev's_lemma.