I've recently come across a divisibility problem that I am unable to solve. I know that most of these types of problems have fairly straightforward proof-by-induction solutions -- but for this particular problem, I don't know how to finish the inductive step. Or perhaps there is another, easier path to a proof?
Anyways here it is:
Prove that ((n+1)^n) - 1 is divisible by n^2 for all positive integers n.
Thanks in advance!