1. ## 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

2. ## Re: Question on divisibility

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 $\displaystyle 2|4~\&~3|9$ so?

3. ## 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

4. ## Re: Question on divisibility

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 $\displaystyle (2+3)|(4+9)~?$

5. ## Re: Question on divisibility

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