About: Ramanujan's congruences

Facets (new session)
Description
Metadata
Settings
- Rule:
- Inverse Functional Properties:
- "Same As":

About: Ramanujan's congruences Goto Sponge NotDistinct Permalink

An Entity of Type : owl:Thing, within Data Space : dbpedia.demo.openlinksw.com associated with source document(s)
QRcode icon

http://dbpedia.demo.openlinksw.com/c/2nEoxvUvc6

In mathematics, Ramanujan's congruences are some remarkable congruences for the partition function p(n). The mathematician Srinivasa Ramanujan discovered the congruences This means that: * If a number is 4 more than a multiple of 5, i.e. it is in the sequence4, 9, 14, 19, 24, 29, . . .then the number of its partitions is a multiple of 5. * If a number is 5 more than a multiple of 7, i.e. it is in the sequence5, 12, 19, 26, 33, 40, . . .then the number of its partitions is a multiple of 7. * If a number is 6 more than a multiple of 11, i.e. it is in the sequence6, 17, 28, 39, 50, 61, . . .then the number of its partitions is a multiple of 11.

Attributes	Values
rdfs:label	Congruences de Ramanujan (fr) ラマヌジャンの合同式 (ja) Ramanujan's congruences (en)
rdfs:comment	In mathematics, Ramanujan's congruences are some remarkable congruences for the partition function p(n). The mathematician Srinivasa Ramanujan discovered the congruences This means that: * If a number is 4 more than a multiple of 5, i.e. it is in the sequence4, 9, 14, 19, 24, 29, . . .then the number of its partitions is a multiple of 5. * If a number is 5 more than a multiple of 7, i.e. it is in the sequence5, 12, 19, 26, 33, 40, . . .then the number of its partitions is a multiple of 7. * If a number is 6 more than a multiple of 11, i.e. it is in the sequence6, 17, 28, 39, 50, 61, . . .then the number of its partitions is a multiple of 11. (en) 整数分割において、ラマヌジャンの合同式（ラマヌジャンのごうどうしき、英: Ramanujan's congruences）は、分割数が満たす整除の関係式。インドの数学者シュリニヴァーサ・ラマヌジャンに因む。ラマヌジャンはイギリスの数学者ゴッドフレイ・ハロルド・ハーディの勧めで渡英し、ハーディとの共同研究の中で分割数を研究した。 (ja) En mathématiques, les congruences de Ramanujan sont des congruences remarquables à propos de la fonction de partition p(n). Le mathématicien Srinivasa Ramanujan a découvert les congruences: Cela signifie que (fr)
dcterms:subject	Equivalence (mathematics) Srinivasa Ramanujan Theorems in number theory
Wikipage page ID	6703729 (xsd:integer)
Wikipage revision ID	1044622775 (xsd:integer)
Link from a Wikipage to another Wikipage	Annals of Mathematics University of Illinois at Chicago Equivalence (mathematics) Srinivasa Ramanujan Theorems in number theory Mathematics Q-Pochhammer symbol Eisenstein series Freeman Dyson G. H. Hardy George Andrews (mathematician) Proceedings of the National Academy of Sciences Combinatorial proof Frank Garvan Hausdorff dimension Karl Mahlburg A. O. L. Atkin American Mathematical Society P-adic number Partition (number theory) Rank of a partition Crank of a partition Ken Ono Srinivasa Ramanujan Ramanujan tau function Crank (mathematics) Proceedings of the Cambridge Philosophical Society
Link from a Wikipage to an external page	https://www.math.ucla.edu/~pak/papers/dyson.htm http://math.mit.edu/~mahlburg/preprints/mahlburg-CrankCong.pdf%7Ctitle= http://www.math.princeton.edu/~annals/issues/2000/151_1.html
sameAs	Ramanujan's congruences Ramanujan's congruences Ramanujan's congruences Ramanujan's congruences Ramanujan's congruences Ramanujan's congruences
dbp:wikiPageUsesTemplate	dbt:Cite_book dbt:Cite_journal dbt:Reflist dbt:Short_description
has abstract	En mathématiques, les congruences de Ramanujan sont des congruences remarquables à propos de la fonction de partition p(n). Le mathématicien Srinivasa Ramanujan a découvert les congruences: Cela signifie que * Si un nombre est congru à 4 modulo 5, c'est-à-dire qu'il est compris dans la suite4, 9, 14, 19, 24, 29, . . .alors le nombre de ses partitions est un multiple de 5. * Si un nombre est congru à 5 modulo 7, c'est-à-dire qu'il est compris dans la suite5, 12, 19, 26, 33, 40, . . .alors le nombre de ses partitions est un multiple de 7. * Si un nombre est congru à 6 modulo 11, c'est-à-dire qu'il est compris dans la suite6, 17, 28, 39, 50, 61, . . .alors le nombre de ses partitions est un multiple de 11. (fr) In mathematics, Ramanujan's congruences are some remarkable congruences for the partition function p(n). The mathematician Srinivasa Ramanujan discovered the congruences This means that: * If a number is 4 more than a multiple of 5, i.e. it is in the sequence4, 9, 14, 19, 24, 29, . . .then the number of its partitions is a multiple of 5. * If a number is 5 more than a multiple of 7, i.e. it is in the sequence5, 12, 19, 26, 33, 40, . . .then the number of its partitions is a multiple of 7. * If a number is 6 more than a multiple of 11, i.e. it is in the sequence6, 17, 28, 39, 50, 61, . . .then the number of its partitions is a multiple of 11. (en) 整数分割において、ラマヌジャンの合同式（ラマヌジャンのごうどうしき、英: Ramanujan's congruences）は、分割数が満たす整除の関係式。インドの数学者シュリニヴァーサ・ラマヌジャンに因む。ラマヌジャンはイギリスの数学者ゴッドフレイ・ハロルド・ハーディの勧めで渡英し、ハーディとの共同研究の中で分割数を研究した。 (ja)
prov:wasDerivedFrom	wikipedia-en:Ramanujan's_congruences?oldid=1044622775&ns=0
page length (characters) of wiki page	7227 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Ramanujan's_congruences
is Link from a Wikipage to another Wikipage of	Jordan Ellenberg Generating function Gifted (2017 film) The Man Who Knew Infinity Partition (number theory) Partition function (number theory) Rank of a partition Congruence Spt function List of things named after Srinivasa Ramanujan Partition congruences and the andrews-garvan-dyson crank Ramanujan's congruence Ramanujan congruences Crank function Partition Congruences and the Andrews-Garvan-Dyson Crank
is Wikipage redirect of	Partition congruences and the andrews-garvan-dyson crank Ramanujan's congruence Ramanujan congruences Crank function Partition Congruences and the Andrews-Garvan-Dyson Crank
is Wikipage disambiguates of	Congruence
is foaf:primaryTopic of	wikipedia-en:Ramanujan's_congruences

Faceted Search & Find service v1.17_git147 as of Sep 06 2024

Alternative Linked Data Documents: ODE Content Formats:

RDF

ODATA

Microdata

About

OpenLink Virtuoso version 08.03.3332 as of Dec 5 2024, on Linux (x86_64-generic-linux-glibc212), Single-Server Edition (378 GB total memory, 50 GB memory in use)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2025 OpenLink Software