Open Question: Fields and Irreducible Polynomials?
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aba Member since:October 19, 2007Total points:284 (Level 2)9. Let F be a field with p^n elements. Show that F has a subfield K with p^m elements if
and only if m | n.
10. Let K be a finite field. Show that the product of all the nonzero elements of K is -1.
11. Write f(x) = x^16 - x in Z2[x] (that is, f(x) = x^2^4- x) as the product of all monic
irreducible polynomials over Z2 of degree dividing 4.
12. (a) Determine the number of monic irreducible polynomials of degree 6 in Z2[x].
(b) Determine the number of monic irreducible polynomials of degree 11 in Z3[x].Answer QuestionBe the first to answer this question.
aba Member since:October 19, 2007Total points:284 (Level 2)9. Let F be a field with p^n elements. Show that F has a subfield K with p^m elements ifand only if m | n.
10. Let K be a finite field. Show that the product of all the nonzero elements of K is -1.
11. Write f(x) = x^16 - x in Z2[x] (that is, f(x) = x^2^4- x) as the product of all monic
irreducible polynomials over Z2 of degree dividing 4.
12. (a) Determine the number of monic irreducible polynomials of degree 6 in Z2[x].
(b) Determine the number of monic irreducible polynomials of degree 11 in Z3[x].Answer QuestionBe the first to answer this question.
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