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.

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- Oct 10th 2010, 03:14 PMkanoroProving 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, 03:55 PMharish21
x|y if y = xk for some k..

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

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

so... - Oct 10th 2010, 04:04 PMkanoro
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, 04:09 PMharish21
$\displaystyle b+c = al $

$\displaystyle b=ak$

so $\displaystyle ak+c = al$

a|c means c = a(an integer)

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