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If p is prime

  1. Oct 24, 2013 #1
    1. The problem statement, all variables and given/known data

    If p is a prime and p>3, show that pr[itex]\equiv[/itex]1,5,7 or 11 (mod12)

    2. Relevant equations



    3. The attempt at a solution
    Do I go about this by knowing that any prime p greater than 3 is of the form 6n+1 or 6n+5? Any direction on how to go about this will be helpful. Thanks.
     
  2. jcsd
  3. Oct 24, 2013 #2

    Dick

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    Show any other possibility doesn't work. For example, suppose ##p^r\equiv 2 (mod 12)##. What's wrong with that?
     
  4. Oct 24, 2013 #3
    If k is an odd number, list the possibilities for k mod 12.
    Next if p is a prime > 3, list the possibilities for p mod 12.
    Then what conclusion can you draw about ##p^r##?
     
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