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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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Theorem

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Reference

## Mathematics Subject Classification

11C08*no label found*

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## Recent Activity

Oct 21

new question: Prime numbers out of sequence by Rubens373

Oct 7

new question: Lorenz system by David Bankom

Oct 19

new correction: examples and OEIS sequences by fizzie

Oct 13

new correction: Define Galois correspondence by porton

Oct 7

new correction: Closure properties on languages: DCFL not closed under reversal by babou

new correction: DCFLs are not closed under reversal by petey

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new correction: Many corrections by Smarandache

Sep 28

new question: how to contest an entry? by zorba

new question: simple question by parag

new question: Prime numbers out of sequence by Rubens373

Oct 7

new question: Lorenz system by David Bankom

Oct 19

new correction: examples and OEIS sequences by fizzie

Oct 13

new correction: Define Galois correspondence by porton

Oct 7

new correction: Closure properties on languages: DCFL not closed under reversal by babou

new correction: DCFLs are not closed under reversal by petey

Oct 2

new correction: Many corrections by Smarandache

Sep 28

new question: how to contest an entry? by zorba

new question: simple question by parag

## Corrections

title by matte ✓

irreducible is a bad link by matte ✓

n is also degree? by Stig Hemmer ✓

spelling by Mathprof ✓

wording; numbering by mps ✓

irreducible is a bad link by matte ✓

n is also degree? by Stig Hemmer ✓

spelling by Mathprof ✓

wording; numbering by mps ✓