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Math Help - gcds

  1. #1
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    gcds

    Let a,b,c are in Z with (a,b)=1 and a divides bc. Prove that a divides c.

    My work:
    ax+by=1
    bc=am

    (ax+by=1)C
    cax+cby=c
    ax(am/b)+by(am/b)=c
    a^2xm/b+amy=c
    a(axm/n+my)=c

    dont know if this is correct?
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  2. #2
    Moo
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    Hello,
    Quote Originally Posted by rmpatel5 View Post
    Let a,b,c are in Z with (a,b)=1 and a divides bc. Prove that a divides c.

    My work:
    ax+by=1
    bc=am

    (ax+by=1)C
    cax+cby=c
    ax(am/b)+by(am/b)=c
    a^2xm/b+amy=c
    a(axm/b+my)=c

    dont know if this is correct?
    Yes it is, but you have to say that \frac{amx}{b}+my is an integer !

    Which is true because am/b=c..

    actually, you could do this way :
    (ax+by=1)*c
    acx+cby=c
    acx+by(am/b)=c << keep acx
    a(cx+my)=c

    cx+my is obviously an integer.
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