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Which elements of z42 are invertibles?

  1. May 11, 2009 #1
    1. The problem statement, all variables and given/known data

    which elements of z42 are invertibles?

    2. Relevant equations



    3. The attempt at a solution

    In my notes I have that invertibles are relatively prime to the order of the group. So I have

    1, 5, 11, 13, 17, 19, 23, 25, 29, 31, 37, 41.

    Is that the case for all groups?
     
  2. jcsd
  3. May 11, 2009 #2

    jbunniii

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    Re: Invertibles

    Is what the case for all groups?

    Interesting fact: Note that 1 is its own inverse. That leaves 11 invertibles, so if you repeatedly remove pairs of invertibles, you have at least one left without a partner, meaning it has to be its own inverse. Which one is it? Is there an easy way to spot it? Is there more than one?
     
  4. May 12, 2009 #3
    Re: Invertibles

    Can you always take the relatively primes and get the invertibles?
     
  5. May 12, 2009 #4

    jbunniii

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    Re: Invertibles

    Yes, but do you know why? Hint: can you apply Fermat's little theorem?
     
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