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    Irreducible Polynomial over a Field

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    5. Find an irreducible polynomial f(x) over the field Z3 with
    Z3[x]/(f(x)) = F243.

    Note that 243 = 3^5 .

    Please explain your reasoning and solution in as much detail as possible.
    Thank You.

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    Solution Summary

    An irreducible polynomial over a given field is found. The solution is detailed and well presented.