It doesn't involve overly impossible combinatorics (which was good) but you'll want to be familiar with n choose k, Pascal's triangle, permutations, combinations, and of course n factorial. And then the principle of inclusion exclusion. Thanks for the find though... it creates a sort of alternating pascal's triangle in terms of the leading coefficients to the powers I may add an additional proof that is a simple generalization of the first part.
The proof is finally up. I started a forum thread on the group for discussion about the proof if you have any questions. It's not extremely pretty looking so hopefully you can read through it, but do ask questions I'd be happy to explain. Oh and be sure to check the captions because the pages appear out of order but I made sure the captions reflected the proper page.
I have a proof relating to your find with the differences of consecutive powers. I will post it in the next day or so once I get it scanned and I'll put it in the forums.
Are you familiar with any combinatorics? The proof relies on combinatorics. And uses Pascal's Identity, and the Principle of Inclusion and Exclusion. Anyways expect to see it up there soon.
LIFE begins at CONCEPTION! (when the zygote has its own unique DNA pattern...)
