1. If a E G has order d, prove that a' also has order d if and only if r and d are relatively prime. 2. Find a cyclic generator (primitive root) for Z. 3. Do Problem 2 for Z. 4. Construct a field K having nine elements and find a cyclic generator for the group K*. 5. If p is a prime and m = {[a] | (a, p) = 1} form a group under the multiplication in Zm. Prove that this group is cyclic of order p (p - 1). p?, then Zm is not a field but the elements

1. If a E G has order d, prove that a' also has order d if and only if r and d are relatively prime. 2. Find a cyclic generator (primitive root) for Z. 3. Do Problem 2 for Z. 4. Construct a field K having nine elements and find a cyclic generator for the group K*. 5. If p is a prime and m = {[a] | (a, p) = 1} form a group under the multiplication in Zm. Prove that this group is cyclic of order p (p - 1). p?, then Zm is not a field but the elements

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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