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Modular arithmetic

  1. Oct 23, 2008 #1
    1. The problem statement, all variables and given/known data

    find: 12^9 mod71

    2. Relevant equations



    3. The attempt at a solution

    =12(12^8) mod71
    = 12mod71 x 12^8mod71
    = 12 x (12^2)^4mod 71

    Now i'm stuck. My teacher solved it but i dont understand what he did so can someone explain how to do it in a very basic way.?
    Thank you v much.
     
  2. jcsd
  3. Oct 23, 2008 #2

    Dick

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    12^2 mod 71=2 mod 71. So 12^8 mod 71=2^4 mod 71.
     
  4. Oct 23, 2008 #3
    how come 12^2mod71=2mod71 ??
     
  5. Oct 23, 2008 #4

    Dick

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    Because 12^2=144. 144 mod 71=2 mod 71.
     
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