A. Cohn’s irreducibility criterion
Theorem.
Assume is an integer and that is a polynomial with coefficients in . If is prime then is irreducible (http://planetmath.org/IrreduciblePolynomial2) in .
A proof is given in [MRM].
A. Cohn [PZ] proved this theorem for the case .
This special case of the above theorem is sketched as problem 128, Part VIII, in [PZ].
References
- PZ George Pólya, Gabor Szego,Problems and Theorems in Analysis II,Classics in Mathematics 1998.
- MRM M. Ram Murty, Prime Numbers and Irreducible Polynomials
, AmericanMathematical Monthly, vol. 109, (2002), 452-458.