I am stuck at a task... I want to determine $n$ of those terms:
$ 1) gcd(n^{1000}(n^2-1))$
$ 2) gcd(n^{1000}(n^4-1)) $
$ 3) gcd(n^{1000}(n^6-1))$
$4) gcd(n^{1000}(n^{12} -1)) $
where $ n \in \mathbb{N} $
What I think the task is about,is to determine the gcd of all numbers of the form f.e $n^{1000}(n^2-1) $ and so on.. How can I do that?
appreciate any help!