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Math · Advanced Math
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Hello,

I need help with problem 4a and 4b.

Please show all the steps and the solutions of the problems.

Thank you very much.

4. Fix a prime integer p. (a) Given a positive integer N, give a formula for the total number Pof polynomials in Zp[ of degree less than or equal to N. If p-2 and N = 100, what is P? (b) Given a positive integer N, prove there is an irreducible polynomial in Zpof degree greater than N. Conclude Zp|r] contains irreducible polynomials of arbitrarily large degree

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