Let Zn be the integers mod n under modular addition. a) What is |Z14|? (Remember what |Ss| means when S is a set!) b) Show that Z14 is cyclic. c) Find all generators of Z14 (see Definition 15.5.5)

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.4: Binary Operations
Problem 9E: 9. The definition of an even integer was stated in Section 1.2. Prove or disprove that the set of...
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Definition 15.5.5. If a group G contains some element a such that G = <a>
then G is a cyclic group. In this case a is a generator of G

Let Zn be the integers mod n under modular addition.
a) What is |Z14|? (Remember what |S| means when S is a set!)
b) Show that Z14 is cyclic.
c) Find all generators of Z14 (see Definition 15.5.5)
Transcribed Image Text:Let Zn be the integers mod n under modular addition. a) What is |Z14|? (Remember what |S| means when S is a set!) b) Show that Z14 is cyclic. c) Find all generators of Z14 (see Definition 15.5.5)
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