How would you prove that, if
is divisible by
(where
is prime and
is an integer), then
is also divisible by
?
For example, if
, then how do you prove that
if is divisible by
,
then is also divisible by
?
I get the feeling this might be blindingly obvious, but then, those are the types of proofs I tend to have trouble on. I know the reason for it intuitively (it has to do with
being prime), but somehow i dont know how to demonstrate it. I guess I would start by saying that
with
being an integer. So then I would want to prove that, if this is true, then
is true also (
being an integer). Is that right? Where would I go from there? A proof by contradiction? I'm still not totally fluent in abstract language, so it takes me a long time to "translate" things.
Thanks!