An elementary proof of the symmetry of power sum polynomials

Key Points

• The polynomial p_{k}(n) is symmetric around x=-1/2 for even k and the point (-1/2,0) for odd k.
• This proof simplifies existing results regarding the symmetrical nature of power sums in polynomials.
• The degree of polynomials under consideration directly influences their symmetry properties.
• Understanding these symmetries can provide insights into the behavior of power sum polynomials.