(10) A group is a set equipped with one (not two) operations, which has an identity with respect to that operation, and for which every element has an inverse in that operation (you can see the definition at the beginning of Chapter 2 of your text). Show that for any n € Z, the units of Zn form a group under multiplication. Specifically, this means showing that the product of any two units is again a unit in Zn. Characterize all the units in Zn.

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(10) A group is a set equipped with one (not two) operations, which has an
identity with respect to that operation, and for which every element has
an inverse in that operation (you can see the definition at the beginning of
Chapter 2 of your text). Show that for any n € Z, the units of Zn form
a group under multiplication. Specifically, this means showing that the
product of any two units is again a unit in Zn.
Characterize all the units in Zn.
Transcribed Image Text:(10) A group is a set equipped with one (not two) operations, which has an identity with respect to that operation, and for which every element has an inverse in that operation (you can see the definition at the beginning of Chapter 2 of your text). Show that for any n € Z, the units of Zn form a group under multiplication. Specifically, this means showing that the product of any two units is again a unit in Zn. Characterize all the units in Zn.
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