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Let α be a zero of x3 + x2 + 1 in some extension field of Z2. Solve the equation (α + 1) x + α = α2 + 1 for x.

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 9E: Let be a field. Prove that if is a zero of then is a zero of

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Let α be a zero of x³ + x² + 1 in some extension field of Z₂. Solve the equation (α + 1) x + α = α² + 1 for x.

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