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Math Help - How do i deal with fractions when using Modulo?

  1. #1
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    How do i deal with fractions when using Modulo?

    For example if i am using Z7, then first and foremost are the following correct?

    -25 = 3

    23 = 2

    (just want to check im using modulo ok)

    Then if i need to simplify 1/2 and 37/2 in Z7, then do i proceed the same? Im just wondering if the numbers have to be integers to use modulo?

    At the minute i am thinkin that:

    1/2 = 1/2 and
    37/2 = 9/2

    are these correct?

    Thanks :-)
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  2. #2
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    For example if i am using Z7, then first and foremost are the following correct?

    -25 = 3

    23 = 2
    That's correct.

    Then if i need to simplify 1/2 and 37/2 in Z7, then do i proceed the same? Im just wondering if the numbers have to be integers to use modulo?
    By definition, 1/2 = 1\cdot 2^{-1}, so the problem is to find the reciprocal of 2 in \mathbb{Z}_7. It is easy to see that 2^{-1}=4 because 2\cdot4\equiv1\pmod{7}. In general, reciprocals can be found using Bézout's identity.
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  3. #3
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    Ah i see, so in this case would i find that:

    1/2 = 4

    and

    37/2 = 1

    ?
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  4. #4
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    Yes.
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