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 PÃÂ³lya, 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.

单词	ACohnsIrreducibilityCriterion
释义	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 PÃÂ³lya, 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.
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