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Math Help - gcd question

  1. #1
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    gcd question

    Question: Show that (ma,mb) = m(a,b) if m if greater than 0.

    Answer: c = (a,b)
    c = xa + yb
    mc = mxa + myb = m(a,b)

    This is where I'm stuck, I'm not sure how to prove that m(a,b) = (ma,mb). I also know that mc|ma and mc|mb.

    Thanks!
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  2. #2
    MHF Contributor kalagota's Avatar
    Joined
    Oct 2007
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    Taguig City, Philippines
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    Quote Originally Posted by temp31415 View Post
    Question: Show that (ma,mb) = m(a,b) if m if greater than 0.

    Answer: c = (a,b)
    c = xa + yb
    mc = mxa + myb = m(a,b)

    This is where I'm stuck, I'm not sure how to prove that m(a,b) = (ma,mb). I also know that mc|ma and mc|mb.

    Thanks!
    i have proved this before but i can't find the thread.. anyways..

    let d = (ma,mb). then d = max + may for some integers x,y..
    notice that, m|max and m|may, thus, m|d..

    so, \frac{d}{m} = ax + by.. hence, \frac{d}{m} = (a,b) \implies d = m(a,b)
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