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单词 ACohnsIrreducibilityCriterion
释义

A. Cohn’s irreducibility criterion


Theorem.

Assume n2 is an integer and that P is a polynomialMathworldPlanetmathPlanetmathPlanetmath with coefficients in {0,1,,n-1}. If P(n) is prime then P(x) is irreducible (http://planetmath.org/IrreduciblePolynomial2) in 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 Pólya, Gabor Szego,Problems and Theorems in Analysis II,Classics in Mathematics 1998.
  • MRM M. Ram Murty, Prime Numbers and Irreducible PolynomialsMathworldPlanetmath, AmericanMathematical Monthly, vol. 109, (2002), 452-458.
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