For which n listed below does there exist a field extension F ɔ Z/2 of degree n such that the polynomial x + X² +1 € F[X] has a root?

Algebra and Trigonometry (6th Edition)
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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For which n listed below does there exist a field extension F ɔ Z/2 of degree n such that the polynomial
x4 + X? +1 € F[X] has a root?
O n = 1
O n = 2
O n = 3
O n = 4
Transcribed Image Text:For which n listed below does there exist a field extension F ɔ Z/2 of degree n such that the polynomial x4 + X? +1 € F[X] has a root? O n = 1 O n = 2 O n = 3 O n = 4
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