Assume A dividesB, and A divides C. Determine if the following statement is true or false and prove your conjecture: A divides B +C

Question

geerky42 · Answer

Since $A$ divides $B$ and $A$ divides $C$, that mean there exist integer $m$ and $n$ such that  $An = B$ and $Am = C$.

$B + C = An + Am = A(n+m)$ therefore $A$ divides $B+C $

anonymous · Answer

Took me time to understand your response but now after reading a few times i get it. Thanks!

anonymous · Answer

@geerky42

geerky42 · Answer

Welcome.

anonymous · Answer

I have a similar problem, so will the answer be similar? 
Assume A divides B, and A divides C. Determine if the following statement is true or false
and prove your conjecture: A divides BC

BC=An*Am=A(n+m) therefore A divides B+C?

anonymous · Answer

@geerky42

anonymous · Answer

Can I use numbers instead of A, B and C to prove?

geerky42 · Answer

Numbers won't really prove anything. All they do are showing that it is true for certain numbers A, B, and C.

You need to prove that it is true for all possible integers.

Yeah, process is similar. You just go like

"$BC=Am\cdot An=A(mn)$ therefore $A$ divides $BC$"

anonymous · Answer

Thanks! @geerky42