Thread: 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

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 so?

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

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

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