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Homework Help: Equivalence class problem

  1. Jun 9, 2010 #1
    1. The problem statement, all variables and given/known data

    Suppose [d], [tex]\in[/tex] Z sub n.
     
    Last edited: Jun 9, 2010
  2. jcsd
  3. Jun 9, 2010 #2

    CompuChip

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    The good news here is, that you can perform all operations in Zm by picking any representative and working in the integers.

    So if c sits in the conjugacy class of a, you can write
    c = a + i m
    where 0 <= a < m and i is some integer, similarly
    d = b + j m
     
  4. Jun 9, 2010 #3

    CompuChip

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    If cd is congruent to ab mod m, then cd lies in [ab] by definition, doesn't it?
    If you want a less trivial proof, show that
    cd = ab + km
    for some integer k.
     
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