# Question on divisibility

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• Nov 26th 2012, 02:10 PM
sakuraxkisu
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 :)
• Nov 26th 2012, 02:24 PM
Plato
Re: Question on divisibility
Quote:

Originally Posted by sakuraxkisu
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?
• Nov 26th 2012, 03:51 PM
sakuraxkisu
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
• Nov 26th 2012, 04:09 PM
Plato
Re: Question on divisibility
Quote:

Originally Posted by sakuraxkisu
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 $(2+3)|(4+9)~?$
• Nov 26th 2012, 04:20 PM
sakuraxkisu
Re: Question on divisibility
Sorry about my stupidity, I feel so silly now haha! Thanks :)