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Math Help - Prove or disprove that (ac,b) =1

  1. #1
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    Prove or disprove that (ac,b) =1

    Let (a,b)=1 and (a,c)=1. Prove or disprove that (ac,b)=1

    this is a common divisor section in abstract algebria.
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  2. #2
    MHF Contributor Swlabr's Avatar
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    Quote Originally Posted by rainyice View Post
    Let (a,b)=1 and (a,c)=1. Prove or disprove that (ac,b)=1

    this is a common divisor section in abstract algebria.
    Let b=c...
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    Quote Originally Posted by Swlabr View Post
    Let b=c...
    what if b does not equal c?
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  4. #4
    MHF Contributor Swlabr's Avatar
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    Quote Originally Posted by rainyice View Post
    what if b does not equal c?
    That doesn't matter. This provides a counter example.

    If you want to look more into this problem, use the fact that a|b implies that there is an x such that ax=b.
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  5. #5
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    Quote Originally Posted by Swlabr View Post
    That doesn't matter. This provides a counter example.

    If you want to look more into this problem, use the fact that a|b implies that there is an x such that ax=b.

    I chose a=11 b=4 and c=8 so that (ac,b) is not equal to 1 but (a,b) and (a,c) are equal to 1
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