anonymous
  • anonymous
"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!?
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
"for SOME integers \(p\) and \(q\)" i meant to add
anonymous
  • anonymous
i don't seem to get why x.x
JamesJ
  • JamesJ
Choose p=q=1

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anonymous
  • anonymous
No we can't make such assumption.
anonymous
  • anonymous
like a=2, b=4, c=3 c|(a+b) -> 3|6 which is true but c|(2a+3b) -> 3|16 is false :(
JamesJ
  • JamesJ
\[ c | (a+b) \implies c | (1\cdot a + 1\cdot b) \]
anonymous
  • anonymous
\(3|(4+5)\) but 3 does not divide \((4\times 3+5 \times 5) \)
anonymous
  • anonymous
ooooh
JamesJ
  • JamesJ
so if the question is there exist at least one pair p,q such your statement is true, then yes.
anonymous
  • anonymous
But this question is asking for for all \(p,q \in \mathbb{Z}\), hence incorrect.
anonymous
  • anonymous
all or any*
JamesJ
  • JamesJ
ffm, pre-algebra says immediately below "for SOME p and q ..."
anonymous
  • anonymous
Hey, EDIT feature is a must!!!!
anonymous
  • anonymous
I have a tendency not to read any comment/answer before trying it on my own.
JamesJ
  • JamesJ
no kidding
anonymous
  • anonymous
"for SOME integers p and q" that's true.

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