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Math Help - Simple Proof Question

  1. #1
    Junior Member
    Joined
    Sep 2010
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    Simple Proof Question

    Given gcd(a,b)=1 and a|bc prove a|c?

    This is what I did, I just want someone to confirm it as I don't have any solutions.

    as+bt=1 (coprime) (1) and bc=ak (2) for some integer s,t and k.

    Multiply (1) by c --> acs+bct=c and use (2) to replace bc with ak

    Then we get acs+akt=c --> factorize a and then we get a|c.

    Is this simple proof enough, or have I missed out on something?

    Thanks
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  2. #2
    MHF Contributor chiph588@'s Avatar
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    Champaign, Illinois
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    Quote Originally Posted by ikurwae89 View Post
    Given gcd(a,b)=1 and a|bc prove a|c?

    This is what I did, I just want someone to confirm it as I don't have any solutions.

    as+bt=1 (coprime) (1) and bc=ak (2) for some integer s,t and k.

    Multiply (1) by c --> acs+bct=c and use (2) to replace bc with ak

    Then we get acs+akt=c --> factorize a and then we get a|c.

    Is this simple proof enough, or have I missed out on something?

    Thanks
    Looks fine to me.
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