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Find an integer n > 1 such that an = a for all a in Z6. Do

Chapter 12, Problem 35E

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QUESTION:

Problem 35E

Find an integer n > 1 such that an = a for all a in Z6. Do the same for Z10. Show that no such n exists for Zm when m is divisible by the square of some prime.

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QUESTION:

Problem 35E

Find an integer n > 1 such that an = a for all a in Z6. Do the same for Z10. Show that no such n exists for Zm when m is divisible by the square of some prime.

ANSWER:

Step 1 of 3

To find an integer  such that for all

Let us choose .

Now, in ,

Therefore, the integer  such that for allis 3.

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