U(20)=(1,3,7,9,11,13,17,19).
ord(20)=8
ord(3)=ord(17)=ord(7)=ord(13)=4,ord(19)=ord(9)=ord(11)=2
So since no element has order 8, no element can generate U(20).\
--Johns121 22:17, 2 February 2009 (UTC)
I am starting to understand the concepts behind these problems now. I wanted to clarify that in order to get U(20) we find all the numbers below twenty that aren't factors of 20? I think this is correct from what he said in lecture and since 2 is a multiple of 20 then that can't be used along with examples like 8 or 12 since 2 is a multiple of those. Another way that I look at how to get U(20) is by seeing that if you pair certain elements in the group then you get 20 as the sum. Examples would be (1+19), (3+17), (7+13), and (9+11) but we just exclude elements that are multiples of 20 and we get the answer U(20). There is a connection between each way of looking at it but for some reason this works faster for me. After seeing your explanation I see why no element can generate U(20). --Nswitzer 17:10, 4 February 2009 (UTC)
