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Math Help - Question on divisibility

  1. #1
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    Question on divisibility

    Is the following statement true in general (for integers a, b, c, d)? Justify your answer, referring to the definition of divisibility.
    If a divides c and b divides d, then (a+b) divides (c+d).

    So far what I've done is say that c=ax and d=by, where x and y are integers.

    I then said that c + d = ax + by, but after this I'm not sure what to do. Any help would be greatly appreciated
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  2. #2
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    Re: Question on divisibility

    Quote Originally Posted by sakuraxkisu View Post
    Is the following statement true in general (for integers a, b, c, d)? Justify your answer, referring to the definition of divisibility.
    If a divides c and b divides d, then (a+b) divides (c+d).

    Well 2|4~\&~3|9 so?
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  3. #3
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    Re: Question on divisibility

    I think I'm supposed to give a proof rather than examples that work, so I don't think that just stating an example would be sufficient. Would you be able to help me? Thanks
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  4. #4
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    Re: Question on divisibility

    Quote Originally Posted by sakuraxkisu View Post
    I think I'm supposed to give a proof rather than examples that work, so I don't think that just stating an example would be sufficient. Would you be able to help me? Thanks
    How can you prove something that is not true?

    Does (2+3)|(4+9)~?
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  5. #5
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    Re: Question on divisibility

    Sorry about my stupidity, I feel so silly now haha! Thanks
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