. Hungerford defines exponentiation in Zn on p. 36. Note that, from that definition, together with the definition of multiplication in Zn (p. 32), it follows that [a]* = [a*] in Zn, for all a E Z and k E Z>1. Compute the following. [52000] in Z4. [42001] in Z5. [39003] in Z7. (a) (b)

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Hungerford defines exponentiation in Zn on p. 36. Note that, from that definition,
together with the definition of multiplication in Zn (p. 32), it follows that [a]k = [a*]
in Zn, for all a E Z and k E Z>1. Compute the following.
[52000] in Z4.
[42001] in Zg.
[39008] in Z7.
(a)
(b)
(c)
Hint: Again, if you're using a calculator or computer to do these problems, you're
missing the point. With a little theory, you can solve these problems using computa-
tions that you easily do in your head!
Transcribed Image Text:Hungerford defines exponentiation in Zn on p. 36. Note that, from that definition, together with the definition of multiplication in Zn (p. 32), it follows that [a]k = [a*] in Zn, for all a E Z and k E Z>1. Compute the following. [52000] in Z4. [42001] in Zg. [39008] in Z7. (a) (b) (c) Hint: Again, if you're using a calculator or computer to do these problems, you're missing the point. With a little theory, you can solve these problems using computa- tions that you easily do in your head!
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