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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. -

2.3. 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. -

Elements Of Modern Algebra
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 9E: Construct a field having the following number of elements.
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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.
Transcribed Image Text: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.
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