Let |a|=30.  How many left cosets of <a4>  in <a> are there?  List them.   I was able to determine that there should be two left cosets, but I'm having trouble identifying them.  I know one is <a4>, but can't seem to reason what the other one is.

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.4: Prime Factors And Greatest Common Divisor
Problem 17E
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Let |a|=30.  How many left cosets of <a4>  in <a> are there?  List them.

 

I was able to determine that there should be two left cosets, but I'm having trouble identifying them.  I know one is <a4>, but can't seem to reason what the other one is.

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