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Math Help - divides and greatest common divisor questions

  1. #1
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    divides and greatest common divisor questions

    This was the question proposed to me. I want to see if I am on the right track. If m|n and p|n and gcd(m,p) = 1 then mp|n.

    Suppose m|n and p|n and gcd(m,p) = 1. We want to prove that mp|n. This means that n = ms and n = pt and 1 = mu + pv for s,t,u,v element of Z. By multiplying both sides by n we obtain:

    1 = mu + pv
    n = nmu +npv
    n = ptmu + mspv
    n = mp(tu + sv)

    Since s,t,u,v are elements of Z. Thus mp|n.
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  2. #2
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    Re: divides and greatest common divisor questions

    Seems OK.
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