4. Prove that 2/2z/a is a field where p(X) = X³ + X + 1 € Z/2z[X] and a == (p(X)).

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Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter8: Polynomials

Section8.3: Factorization In F [x]

Problem 22E: Let ab in a field F. Show that x+a and x+b are relatively prime in F[x].

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Prove that 2/27/a is a field where p(X) = X³ + X + 1 € Z/2z[X] and a = = (p(X)).