# Math Help - Proving a|(b+c) and a|b, then a|c

1. ## Proving a|(b+c) and a|b, then a|c

Hi, working on a problem and need some help.. The problem is that if a,b,c are integers and a|(b+c) and a|b, then a|c. Thanks in advance.

2. x|y if y = xk for some k..

$a|b \implies b = ak$ for some k

$a|(b+c) \implies (b+c) = al$ for some l

so...

3. Right, so then I get b + c = al for some l and b = al2 for some l2 right. So then do I add the two equations together or what?

4. $b+c = al$

$b=ak$

so $ak+c = al$

a|c means c = a(an integer)

....