Exercise 6.3.13(a) Assume p is prime. Show that there are (p - 1)/2 irreducible polynomials of the formf(x) = x – b in Z,[r].(b) Show that for every prime p, there exists a field with p2 elements.There is actually a formula for the number of irreducible polynomials of degree d overZ, or any finite field. See Dornhoff and Hohn [25, p. 377].

The given question is related with abstract algebra. (a) Assume p is a prime. We have to show…

Answered: (a) Assume p is prime. Show that there…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter8: Polynomials

Section8.6: Algebraic Extensions Of A Field

Problem 7E

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(a) Assume p is prime. Show that there are (p- 1)/2 irreducible polynomials of the form f(x) = x² – b in Z,[r]. (b) Show that for every prime p, there exists a field with p2 elements.