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Units for finite fields

  1. Feb 25, 2009 #1
    1. The problem statement, all variables and given/known data

    Suppose that m = 1 mod b. What integer between 1 and m-1 is equal to b^(-1) mod m?

    3. The attempt at a solution

    m = 1 mod b means that:

    m = kb + 1 for some integer k

    Let x be the inverse of b mod m, note: x exists since b and m must be coprime due to the previous statement.

    xb = 1 mod m

    thus: xb = gm + 1 for some integer g.

    Now this is were I have little success. I cant seem to manipulate anything to my advantage and I'm unsure how to proceed.

    I did find x = (m+1)/b but that is not always an integer. Thanks for any help you can provide.
     
  2. jcsd
  3. Feb 25, 2009 #2

    Hurkyl

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    Well, you don't seem to have made use of the fact that m = 1 mod b....
     
  4. Feb 26, 2009 #3
    I thought I used that fact when using the statement

    m = kb + 1 for some integer k, unless I'm missing something else. Little tired, but I will come back to it tomorrow.
     
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