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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Originally Posted by page929 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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