Quote:
Originally Posted by devarajkandadai
Merely saying " I am pretty sure Isaac....." will not do; can you quote any paper or book where in either Newton, Euler or any mathematician has mentioned this result?

This will not do.
You are making a claim of priority. It is incumbent on
you to check the literature. I suggested Newton, whose work with polynomials is well known, both WRT derivatives of powers and "Newton's identities," but you refused to look. It is reasonable to conclude that won't look because you're afraid of what you might find.
I
do know that in high school algebra, one of the exercises for learning mathematical induction was to prove that,
for any positive integer n, a  b divides a^n  b^n.
And while I will
not claim that back then we were doing our homework with a stylus on damp clay, I
will say that it was quite a number of years ago. So a result of which (a corrected form of) the one you claim is a trivial corollary, was relegated to the exercises in high school algebra long since. No mathematician worthy of the name would presume to claim it as an original result.
The result I mention is also often used to prove the formula for summing a geometric series. That's been known for a while, too.