Matches in DBpedia 2014 for { ?s ?p 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.. }
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- 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.".