# A. Cohn’s irreducibility criterion

###### Theorem.

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

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].

## References

• PZ George PÃÂ³lya, Gabor Szego, Problems and Theorems in Analysis II, Classics in Mathematics 1998.
• MRM M. Ram Murty, Prime Numbers and Irreducible Polynomials, American Mathematical Monthly, vol. 109, (2002), 452-458.
Title A. Cohn’s irreducibility criterion ACohnsIrreducibilityCriterion 2013-03-22 14:37:02 2013-03-22 14:37:02 Mathprof (13753) Mathprof (13753) 17 Mathprof (13753) Theorem msc 11C08