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Math Help - Automorphisim

  1. #1
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    Automorphisim

    Suppose that ф: Z50 → Z50 is an automorphisim with ф(11) = 13. Determine a formula for ф(x).
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  2. #2
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    Quote Originally Posted by bethh View Post
    Suppose that ф: Z50 → Z50 is an automorphisim with ф(11) = 13. Determine a formula for ф(x).

    Hint: 11 is a generator of Z50. Can you then find ф(1)?
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  3. #3
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    Well ф(1)=11^-1 x 13 but i'm not sure what to do after that.
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  4. #4
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    Quote Originally Posted by bethh View Post
    Well ф(1)=11^-1 x 13 but i'm not sure what to do after that.

    How did you get that? You need to be careful when you are using symbols ^ and x

    Can you express 1 as a power of 11? (Note: by power here we mean repeated application of group operation so 11^5 = 5). Say it is 'n'

    Once you know that ф(1)= ф(11^n) = ф(11)^n

    Once we know ф(1), ф(x) should be easy, right?
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