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

Printable View

• Oct 10th 2010, 04:14 PM
kanoro
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.
• Oct 10th 2010, 04:55 PM
harish21
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...
• Oct 10th 2010, 05:04 PM
kanoro
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?
• Oct 10th 2010, 05:09 PM
harish21
$b+c = al$

$b=ak$

so $ak+c = al$

a|c means c = a(an integer)

....