Thread: Prove a/b and a/c then a/ (3b-7c)

I have to prove that a/b and a/c then a/ (3b-7c), where a, b, and c are integers. I know this is true but I need help with the proof.

Do I assume a does not /(3b-7c)?

I am so lost....please help

I assume that a/b means "a divides b". A vertical bar usually denotes "divides".

If a divides b, then b = k * a for some integer k, and similarly for c. Now, both b and c are expressed through a, so 3b - 7c can also be expressed through a.

Thanks!