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## Homework Statement

List the elements of the subgroups <3> and <7> in U(20).

## Homework Equations

## The Attempt at a Solution

U(20)= {1, 3, 7, 9, 11, 13, 17, 19} = <3> = <7>.

So basically I have that the common elements of, <3> and <7> and U(20), under + modulo 20, are all the elements in U(20). Other than calculating this all out, I reasoned it to be true since 3 and 7 are both coprime to 20.

The answer key in the book has <3>=<7>= {3,9,7,1}.

I believe this is a typo, and that either the answer key is incorrect, or U(20) should be U(10).

Can someone please confirm my suspicion or let me know if I am missing something?