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Math Help - proof about ....

  1. #1
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    proof about ....

    the notation a≡b (mod n) to mean that a and b are both represented by
    the same element of Zn (under addition (mod n)). Show that a≡b (mod n) if and only if n divide (b-a)
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  2. #2
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    Assume a \equiv b (mod n), then by definition a = s \cdot n and b = r \cdot n for  s,r \in \mathbb{N}.

    Now, you can see that b-a = rn - sn = (r-s)n = t \cdot n for some t \in \mathbb{N}, thus n|(b-a).

    Now, for the second part: n|(b-a) \Rightarrow b-a = k \cdot n \Rightarrow b = kn + a \Rightarrow b \equiv a (mod n).
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  3. #3
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    Double post, Delete please..
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