Matches in DBpedia 2014 for { <http://dbpedia.org/resource/Cohn's_irreducibility_criterion> ?p ?o. }
Showing items 1 to 31 of
31
with 100 items per page.
- Cohn's_irreducibility_criterion abstract "Arthur Cohn's irreducibility criterion is a sufficient condition for a polynomial to be irreducible in —that is, for it to be unfactorable into the product of lower-degree polynomials with integer coefficients.The criterion is often stated as follows:If a prime number is expressed in base 10 as (where ) then the polynomialis irreducible in .The theorem can be generalized to other bases as follows:Assume that is a natural number and is a polynomial such that . If is a prime number then is irreducible in .The base-10 version of the theorem attributed to Cohn by Pólya and Szegő in one of their books while the generalization to any base, 2 or greater, is due to Brillhart, Filaseta, and Odlyzko.In 2002, Ram Murty gave a simplified proof as well as some history of the theorem in a paper that is available online.The converse of this criterion is that, if p is an irreducible polynomial with integer coefficients that have greatest common divisor 1, then there exists a base such that the coefficients of p form the representation of a prime number in that base; this is the Bunyakovsky conjecture and its truth or falsity remains an open question.".
- Cohn's_irreducibility_criterion wikiPageID "5984147".
- Cohn's_irreducibility_criterion wikiPageRevisionID "598525238".
- Cohn's_irreducibility_criterion hasPhotoCollection Cohn's_irreducibility_criterion.
- Cohn's_irreducibility_criterion id "6194".
- Cohn's_irreducibility_criterion title "A. Cohn's irreducibility criterion".
- Cohn's_irreducibility_criterion subject Category:Polynomials.
- Cohn's_irreducibility_criterion subject Category:Theorems_in_algebra.
- Cohn's_irreducibility_criterion type Abstraction100002137.
- Cohn's_irreducibility_criterion type Communication100033020.
- Cohn's_irreducibility_criterion type Function113783816.
- Cohn's_irreducibility_criterion type MathematicalRelation113783581.
- Cohn's_irreducibility_criterion type Message106598915.
- Cohn's_irreducibility_criterion type Polynomial105861855.
- Cohn's_irreducibility_criterion type Polynomials.
- Cohn's_irreducibility_criterion type Proposition106750804.
- Cohn's_irreducibility_criterion type Relation100031921.
- Cohn's_irreducibility_criterion type Statement106722453.
- Cohn's_irreducibility_criterion type Theorem106752293.
- Cohn's_irreducibility_criterion type TheoremsInAlgebra.
- Cohn's_irreducibility_criterion comment "Arthur Cohn's irreducibility criterion is a sufficient condition for a polynomial to be irreducible in —that is, for it to be unfactorable into the product of lower-degree polynomials with integer coefficients.The criterion is often stated as follows:If a prime number is expressed in base 10 as (where ) then the polynomialis irreducible in .The theorem can be generalized to other bases as follows:Assume that is a natural number and is a polynomial such that .".
- Cohn's_irreducibility_criterion label "Cohn's irreducibility criterion".
- Cohn's_irreducibility_criterion label "Critère d'irréductibilité de Cohn".
- Cohn's_irreducibility_criterion sameAs Critère_d'irréductibilité_de_Cohn.
- Cohn's_irreducibility_criterion sameAs 콘의_기약성_기준.
- Cohn's_irreducibility_criterion sameAs m.0fj2d9.
- Cohn's_irreducibility_criterion sameAs Q2269888.
- Cohn's_irreducibility_criterion sameAs Q2269888.
- Cohn's_irreducibility_criterion sameAs Cohn's_irreducibility_criterion.
- Cohn's_irreducibility_criterion wasDerivedFrom Cohn's_irreducibility_criterion?oldid=598525238.
- Cohn's_irreducibility_criterion isPrimaryTopicOf Cohn's_irreducibility_criterion.