A. Cohn’s irreducibility criterion

Theorem.

Assume $n\mathrm{\ge }\mathrm{2}$ is an integer and that $P$ is a polynomial with coefficients in $\mathrm{\{}\mathrm{0}\mathrm{,}\mathrm{1}\mathrm{,}\mathrm{\dots }\mathrm{,}n\mathrm{-}\mathrm{1}\mathrm{\}}$. If $P\mathit{}\mathrm{(}n\mathrm{)}$ is prime then $P\mathit{}\mathrm{(}x\mathrm{)}$ is irreducible (http://planetmath.org/IrreduciblePolynomial2) in $\mathrm{Z}\mathit{}\mathrm{[}x\mathrm{]}$.

A proof is given in [MRM].

A. Cohn [PZ] proved this theorem for the case $n=10$.

This special case of the above theorem is sketched as problem 128, Part VIII, in [PZ].

Title	A. Cohn’s irreducibility criterion
Canonical name	ACohnsIrreducibilityCriterion
Date of creation	2013-03-22 14:37:02
Last modified on	2013-03-22 14:37:02
Owner	Mathprof (13753)
Last modified by	Mathprof (13753)
Numerical id	17
Author	Mathprof (13753)
Entry type	Theorem
Classification	msc 11C08