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Math Help - if p divides x then is xy(mod p) = 0 ?

  1. #1
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    if p divides x then is xy(mod p) = 0 ?

    I believe I am correct but I am hoping to get some confirmation...

    is it true that...

    if p|x then xy(mod p) = 0 ?

    I need this for a proof and I just want to make sure it is correct before I go any further.
    Last edited by mr fantastic; October 11th 2011 at 04:15 AM. Reason: Deleted excess ? in title.
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  2. #2
    Senior Member roninpro's Avatar
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    Re: if p divides x then is xy(mod p) = 0 ?

    I think that you can answer your question by answering something more basic: what does it mean to take a number N modulo p?
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  3. #3
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    Re: if p divides x then is xy(mod p) = 0 ?

    you may also find it instructive to recall that p|x means x = pk for some integer k, so xy = (pk)y = p(ky),

    so (xy) mod p = p(ky) mod p = (p mod p)(ky mod p).
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