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Math Help - Proving a|(b+c) and a|b, then a|c

  1. #1
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    Proving a|(b+c) and a|b, then a|c

    Hi, working on a problem and need some help.. The problem is that if a,b,c are integers and a|(b+c) and a|b, then a|c. Thanks in advance.
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  2. #2
    MHF Contributor harish21's Avatar
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    x|y if y = xk for some k..



     a|b \implies b = ak for some k

     a|(b+c) \implies (b+c) = al for some l

    so...
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  3. #3
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    Right, so then I get b + c = al for some l and b = al2 for some l2 right. So then do I add the two equations together or what?
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  4. #4
    MHF Contributor harish21's Avatar
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     b+c = al

     b=ak

    so ak+c = al

    a|c means c = a(an integer)

    ....
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