Let a be a zero of the polynomial x² – 2 € Z5 [x] in some extension field of Z5 and letF = Z5(a).(a) Find a basis for F as a vector space over Z5. How many elements does F have?

Answered: Let a be a zero of the polynomial x² −…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Let a be a zero of the polynomial x² − 2 € Z5[x] in some extension field of Z5 and let F = Z5(α). (a) Find a basis for F as a vector space over Z5. How many elements does ♬ have?