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How many elements of order 4 does Z4 Z4 have (Do not do

Chapter 8, Problem 11E

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QUESTION:

Problem 11E

How many elements of order 4 does Z4 ⊕ Z4 have? (Do not do this by examining each element.) Explain why Z4 ⊕ Z4 has the same number of elements of order 4 as does Z8000000 ⊕ Z400000. Generalize to the case Zm Zn.

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QUESTION:

Problem 11E

How many elements of order 4 does Z4 ⊕ Z4 have? (Do not do this by examining each element.) Explain why Z4 ⊕ Z4 has the same number of elements of order 4 as does Z8000000 ⊕ Z400000. Generalize to the case Zm Zn.

ANSWER:

                                                   

Step 1 of 8

Let  with

Then we obtain  and

                                                   

 

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