Solution Found!
How many elements of order 4 does Z4 Z4 have (Do not do
Chapter 8, Problem 11E(choose chapter or problem)
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.
Questions & Answers
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