A. Cohn’s irreducibility criterion


Assume n2 is an integer and that P is a polynomialMathworldPlanetmathPlanetmathPlanetmath with coefficients in {0,1,,n-1}. If P(n) is prime then P(x) is irreducible (http://planetmath.org/IrreduciblePolynomial2) in Z[x].

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].


  • PZ George Pólya, Gabor Szego, Problems and Theorems in Analysis II, Classics in Mathematics 1998.
  • MRM M. Ram Murty, Prime Numbers and Irreducible PolynomialsMathworldPlanetmath, American Mathematical Monthly, vol. 109, (2002), 452-458.
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