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when are polynomials prime?

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  • Kermit Rose
    Message: 1 Date: Sun, 02 Apr 2006 17:11:26 -0000 From: gordon_as_number Subject: primes of polynomials If you want to prove a
    Message 1 of 1 , Apr 4, 2006
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      Message: 1
      Date: Sun, 02 Apr 2006 17:11:26 -0000
      From: "gordon_as_number" <gordon_as_number@...>
      Subject: primes of polynomials


      If you want to prove a polynomials P(x) is prime,
      isnt enough to determine the assoiated roots.



      Kermit says:

      Gordon, it's an elementary theorem that a polynomial in integer coeficients


      of degree M is prime in the integers provided

      its value is a prime integer sufficiently often.

      I don't remember at the moment whether the critical number of primes is

      M+1 or 2 M or 2 M + 1.


      At least I can assure you that if a polynomial of degree M with integer
      coeficients takes on
      2 M + 1 prime integer values, then that polynomial must be prime in the
      integers.


      It might be sufficient to take on M+1 values, but I don't feel sure about
      that.
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