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Math Help - Modulo arithmetic

  1. #1
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    Modulo arithmetic

    Hey, just stuck on this question:

    Show that in Z_m we have (m-1)^{-1} = m-1

    I have no idea. Please help!  Z is used to represent the set of integers.
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  2. #2
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    Quote Originally Posted by Joel24 View Post
    Hey, just stuck on this question:

    Show that in Z_m we have (m-1)^{-1} = m-1

    I have no idea. Please help!  Z is used to represent the set of integers.
    Well there exists only one multiplicative inverse to any element of \mathbb{Z}_m. So let's find out if the identity works:
    (m - 1)^{-1}(m - 1) = (m - 1)(m - 1) = m^2 - 2m + 1 \equiv 1~\text{mod m}

    It looks like the original assumption is true.

    -Dan
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  3. #3
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    Yes, that makes sense. Thanks a lot Dan.
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