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Find all values of a in Z7 such that the quotient ring Z7[x]/(p(x)) where p(x) = x³ + x² + ax + 3 is a field.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter8: Polynomials

Section8.6: Algebraic Extensions Of A Field

Problem 14E

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Find all values of a in Z7 such that the quotient
ring Z7[x]/(p(x)) where
p(x) = x³ + x² + ax + 3 is a field.
1
Оз
О5
O 2
О6
оо
O 4

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