Show that x^2 + x + 1 has a zero in some extension field of Z_2 that is a simple extension.

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter6: More On Rings
Section6.3: The Characteristic Of A Ring
Problem 8E: 8. Prove that the characteristic of a field is either 0 or a prime.
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Show that x^2 + x + 1 has a zero in some extension field of Z_2 that is a simple extension.

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