On the Sums of Powers of Chebyshev Polynomials and Their Divisible Properties

الملخص EN

The main purpose of this paper is using mathematical induction and the Girard and Waring formula to study a problem involving the sums of powers of the Chebyshev polynomials and prove some divisible properties.

We obtained two interesting congruence results involving Fibonacci numbers and Lucas numbers as some applications of our theorem.