The power sum of balancing polynomials and their divisible properties

Abstract

In recent years, many scholars have studied the division properties of polynomials and sequence power sums. In this paper, we use Girard-Waring formula and combinatorial method to study the power sum problem of balancing polynomials and Lucas-balancing polynomials, and then study the division of balancing polynomials and Lucas-balancing polynomials by mathematical induction and the properties of polynomials.

Keywords

• balancing polynomials
• lucas-balancing polynomials
• power sum problem
• divisible properties