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Math Help - Irreducibility in Zp

  1. #1
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    Irreducibility in Zp

    Could you please help with this problem:

    Show that there are infinitely many irreducible polynomials in Zp[x], where p is prime.

    Deduce that there are infinitely many non-isomorphic finite fields of order a power of p.
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  2. #2
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    Quote Originally Posted by Mimi89 View Post
    Could you please help with this problem:

    Show that there are infinitely many irreducible polynomials in Zp[x], where p is prime.

    Deduce that there are infinitely many non-isomorphic finite fields of order a power of p.

    Mimick Euclides' proof for primes in \mathbb{N}: suppose p_1(x),\ldots,p_n(x) are all the irreducible polynomials in \mathbb{Z}_p[x] ,and define p(x)=p_1(x)\cdot\ldots\cdot p_n(x)+1 ...

    Tonio
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