Cohn's irreducibility criterion [SEP] named after
Cohn's irreducibility criterion
Arthur Cohn's irreducibility criterion is a sufficient condition for a polynomial to be irreducible in formula_1—that is, for it to be unfactorable into the product of lower-degree polynomials with integer coefficients.
The criterion is often stated as follows:
The theorem can be generalized to other bases as follows:
The base-10 version of the theorem is attributed to Cohn by Pólya and Szegő in one of their books while the generalization to any base"b" is due to Brillhart, Filaseta, and Odlyzko.
- Hilbert's irreducibility theorem
- Cohn's irreducibility criterion
- Irreducible component of a topological space
- Factorization of polynomials over finite fields
- Casus irreducibilis, the irreducible cubic with three real roots
References.
- . This classical book covers most of the content of this article.
- , pp. 91.
- , pp. 154.
External links.
- Information on Primitive and Irreducible Polynomials, The (Combinatorial) Object Server.