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Math Help - Irreducible polynomials

  1. #1
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    Irreducible polynomials

    Let F be a finite field. Show that F[x] has irreducible polynomials of arbitrarily high degree.

    I am completely lost. Any help would be great. Thanks!
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  2. #2
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    Quote Originally Posted by page929 View Post
    Let F be a finite field. Show that F[x] has irreducible polynomials of arbitrarily high degree.

    I am completely lost. Any help would be great. Thanks!

    In F[x] , irreducible polynomial = prime elements (why?), and then you can mimic Archimedes' proof of an infinite

    number of prime numbers in the naturals.

    Tonio
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