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# 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 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 PÃ³lya, 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.

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## Mathematics Subject Classification

11C08*no label found*

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## Corrections

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n is also degree? by Stig Hemmer ✓

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