2.1. Construct the group under modulo-6 addition. 2.2. Construct the group under modulo-3 multiplication. 2.3. Let m be a positive integer. If m is not a prime, prove that the set {1, 2, ..., m- 1} is not a group under modulo-m multiplication. 2.4. Construct the prime field GF(11) with modulo-11 addition and multiplication. Find all the primitive elements and determine the orders of other elements.

2.1. Construct the group under modulo-6 addition. 2.2. Construct the group under modulo-3 multiplication. 2.3. Let m be a positive integer. If m is not a prime, prove that the set {1, 2, ..., m- 1} is not a group under modulo-m multiplication. 2.4. Construct the prime field GF(11) with modulo-11 addition and multiplication. Find all the primitive elements and determine the orders of other elements.

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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