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  1. #1
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    definitions

    why is it not true for all positive intergers a,b,c that if ab l c then a l c ?
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  2. #2
    MHF Contributor Swlabr's Avatar
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    Quote Originally Posted by alexandrabel90 View Post
    why is it not true for all positive intergers a,b,c that if ab l c then a l c ?
    (ab)k=c \Rightarrow a(bk) = c \Rightarrow a|c.

    Why do you think this is false?
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  3. #3
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    Quote Originally Posted by alexandrabel90 View Post
    why is it not true for all positive intergers a,b,c that if ab l c then a l c ?
    No one can answer that because it is true that if ab divides c, the a divides c (and, of course, so does b). You may be thinking of the other way around. if c|ab, then it not necessarily true that c|a or c|b. For example, if c= 4, a= 2, b= 6, 4 divides ab= 12 but does not divide either 2 or 6. 4= 2(2)contains a factor from 2 and from 6.
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  4. #4
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    i thought it was true too...but in a maths question that i was given:

    is the following true for all positive intergers a, b ,c?
    (a) a l bc and b is not divisible by a then a l c
    (b) if ab + 1 = c^2 then a and c are coprime
    (c) if ab l c then a l c

    im sure that (a) is true..so i thought that means (b) and (c) are false...is there a mistake in the answer? both (a) and (c) are true right?
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  5. #5
    MHF Contributor Swlabr's Avatar
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    Quote Originally Posted by alexandrabel90 View Post
    i thought it was true too...but in a maths question that i was given:

    is the following true for all positive intergers a, b ,c?
    (a) a l bc and b is not divisible by a then a l c
    (b) if ab + 1 = c^2 then a and c are coprime
    (c) if ab l c then a l c

    im sure that (a) is true..so i thought that means (b) and (c) are false...is there a mistake in the answer? both (a) and (c) are true right?
    The question is asking you to verify if each of the propositions are correct or not. It is, I suppose, badly worded, but essentially you have to answer the three parts individually.

    I suspect the "Is" should be an "Are", although my grammar isn't very good...
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