4. Find all the element of Z/8 that have order 8. Find all the elements of Z/9 that have order 9. Find all the elements of Z/72 that have order 72. (Fun fact: there is a relationship involving the number of elements you find in these three tasks. We will discuss this later in the course.)
4. Find all the element of Z/8 that have order 8. Find all the elements of Z/9 that have order 9. Find all the elements of Z/72 that have order 72. (Fun fact: there is a relationship involving the number of elements you find in these three tasks. We will discuss this later in the course.)
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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I need help with number 4
Transcribed Image Text:**Transcription for Educational Website:**
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**4.** Find all the elements of \( \mathbb{Z}/8 \) that have order 8. Find all the elements of \( \mathbb{Z}/9 \) that have order 9. Find all the elements of \( \mathbb{Z}/72 \) that have order 72. (Fun fact: there is a relationship involving the number of elements you find in these three tasks. We will discuss this later in the course.)
**5.**
(a) Let \( G \) be an abelian group (with the binary operation written as multiplication).
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*Note: The transcription maintains clarity for educational purposes, including mathematical notation using LaTeX for precision and readability.*
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In this question, we have to find all the elements of that have order 8, all the elements of that have order 9 and all the elements of that have that have order 72.
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