Exercise 6.3.13 (a) Assume p is prime. Show that there are (p - 1)/2 irreducible polynomials of the form f(x) = x – b in Z,[r]. (b) Show that for every prime p, there exists a field with p2 elements....

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

Extracted text: Exercise 6.3.13 (a) Assume p is prime. Show that there are (p - 1)/2 irreducible polynomials of the form f(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 over Z, or any finite field. See Dornhoff and Hohn [25, p. 377].

Jun 04, 2022

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Exercise 6.3.13 (a) Assume p is prime. Show that there are (p - 1)/2 irreducible polynomials of the form f(x) = x – b in Z,[r]. (b) Show that for every prime p, there exists a field with p2 elements....

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