A New Method to Express Sums of Power of Integers as a Polynomial Equation

This is a new method to express The power sums of $(n^m)$ as a $(m+1)th-degree$ polynomial equation of n, there is some methods like "Faulhaber's formula" and others gives the solution of the power sums. nevertheless my method is doing the same but it does not depend on Bernoulli numbers or integrals as it is a simple algebraic way giving a polynomial equation and proved in a elementary algebraic logic.
And although I uploaded this paper in 2012 I found after that may be similar method on Wikipedia but this paper has interesting furmula and I hope you injoy reading its proof.

Click here to download the paper.