Irreducible Polynomials
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I need to find the irreducible polynomial in Z3[x].
A) how many irreducible polynomial of degree 2 in Z3[x]
B) how many irreducible polynomial of degree 3 in Z3[x]
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Solution Summary
Irreducible polynomials are investigated.
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There is the following result for which Fermat's little theorem is a special case of. The proof is not reproduced here. If you are interested the proof that result you can consider the book referred or ( On full page of a little advanced algebra) do let me know.
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Let F_q be any finite field on q elements.
For any d >= 1, ((x)^q)^d - x is the product of all monic irreducible polynomials in F_q[x] whose degree divides 'd'.
( ...
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