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The problem says show that U(20) does not equal <k> for any k in U(20). [Hence U(20) is not cyclic.]  
 
The problem says show that U(20) does not equal <k> for any k in U(20). [Hence U(20) is not cyclic.]  
I was trying to understand Example 1 from the text book. where it discusses U(15).
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I was trying to understand Example 1 from the Chapter 3 in the text book. where it discusses U(15).
I am completely confused about where this comes from.
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I am completely confused about what it is talking about:
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U(15) = {1, 2, 4, 7, 8, 11, 13, 14 }
 
U(15) = {1, 2, 4, 7, 8, 11, 13, 14 }
Then it goes on to say
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Then it goes on to say to find the order of element 7, so |7| = 4
<math>7^1 </math>
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<math>7^1 = 7 7^2 =4 7^3 = 13  7^4 = 1</math>

Revision as of 18:07, 15 September 2008

The problem says show that U(20) does not equal <k> for any k in U(20). [Hence U(20) is not cyclic.] I was trying to understand Example 1 from the Chapter 3 in the text book. where it discusses U(15). I am completely confused about what it is talking about:

U(15) = {1, 2, 4, 7, 8, 11, 13, 14 } Then it goes on to say to find the order of element 7, so |7| = 4 $ 7^1 = 7 7^2 =4 7^3 = 13 7^4 = 1 $

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