## anonymous 4 years ago "suppose $$c|(a+b)$$ where $$a,b,c\in\mathbb{Z}$$. then $$c|(pa+qb)$$ where $$p,q\in\mathbb{Z}$$." can you really make such assumption!?

1. anonymous

"for SOME integers $$p$$ and $$q$$" i meant to add

2. anonymous

i don't seem to get why x.x

3. JamesJ

Choose p=q=1

4. anonymous

No we can't make such assumption.

5. anonymous

like a=2, b=4, c=3 c|(a+b) -> 3|6 which is true but c|(2a+3b) -> 3|16 is false :(

6. JamesJ

$c | (a+b) \implies c | (1\cdot a + 1\cdot b)$

7. anonymous

$$3|(4+5)$$ but 3 does not divide $$(4\times 3+5 \times 5)$$

8. anonymous

ooooh

9. JamesJ

so if the question is there exist at least one pair p,q such your statement is true, then yes.

10. anonymous

But this question is asking for for all $$p,q \in \mathbb{Z}$$, hence incorrect.

11. anonymous

all or any*

12. JamesJ

ffm, pre-algebra says immediately below "for SOME p and q ..."

13. anonymous

Hey, EDIT feature is a must!!!!

14. anonymous

I have a tendency not to read any comment/answer before trying it on my own.

15. JamesJ

no kidding

16. anonymous

"for SOME integers p and q" that's true.