Question

"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!?

Answer 1

"for SOME integers \(p\) and \(q\)" i meant to add

Answer 2

i don't seem to get why x.x

Answer 3

Choose p=q=1

Answer 4

No we can't make such assumption.

Answer 5

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

Answer 6

\[ c | (a+b) \implies c | (1\cdot a + 1\cdot b) \]

Answer 7

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

Answer 8

ooooh

Answer 9

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

Answer 10

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

Answer 11

all or any*

Answer 12

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

Answer 13

Hey, EDIT feature is a must!!!!

Answer 14

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

Answer 15

no kidding

Answer 16

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