## Question

###### Find an irreducible polynomial f (z) Z,[z] degree Justify your answer.(b) Let root of the polynomial you found in the previous item in an extension of Z; What is the cardinality of F = Zs(a)?With & as in the previous item find the minimal polynomial of 1/& and a2 +1 over Z;Determine the number of monic cubic irreducible polynomials over Z;

Find an irreducible polynomial f (z) Z,[z] degree Justify your answer. (b) Let root of the polynomial you found in the previous item in an extension of Z; What is the cardinality of F = Zs(a)? With & as in the previous item find the minimal polynomial of 1/& and a2 +1 over Z; Determine the number of monic cubic irreducible polynomials over Z;

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