scholarly journals Some Identities Involving Chebyshev Polynomials

2015 ◽  
Vol 2015 ◽  
pp. 1-5 ◽  
Author(s):  
Xiaoxue Li
Keyword(s):  
Chebyshev Polynomials ◽  
Combinatorial Method ◽  
Sums Of Powers ◽  
Divisibility Properties

The main purpose of this paper is using the combinatorial method and algebraic manipulations to study some sums of powers of Chebyshev polynomials and give several interesting identities. As some applications of these results, we obtained several divisibility properties involving Chebyshev polynomials.

On the rate of p-adic convergence of sums of powers of binomial coefficients

2017 ◽  
Vol 13 (08) ◽  
pp. 2075-2091 ◽  
Author(s):  
Tamás Lengyel
Keyword(s):  
Point Of View ◽  
Binomial Coefficients ◽  
Arithmetic Properties ◽  
Sums Of Powers ◽  
Divisibility Properties

Let [Formula: see text] be an integer and [Formula: see text] be an odd prime. We study sums and lacunary sums of [Formula: see text]th powers of binomial coefficients from the point of view of arithmetic properties. We develop new congruences and prove the [Formula: see text]-adic convergence of some subsequences and that in every step we gain at least one or three more [Formula: see text]-adic digits of the limit if [Formula: see text] or [Formula: see text], respectively. These gains are exact under some explicitly given conditions. The main tools are congruential and divisibility properties of the binomial coefficients and multiple and alternating harmonic sums.

scholarly journals On Power Sums Involving Lucas Functions Sequences

2017 ◽  
Vol 2017 ◽  
pp. 1-11
Author(s):  
Stefano Barbero
Keyword(s):  
Chebyshev Polynomials ◽  
Power Sums ◽  
Polynomial Sequences ◽  
Divisibility Properties

We present some general formulas related to sum of powers, also with alternating sign, involving Lucas functions sequences. In particular, our formulas give a synthesis of various identities involving sum of powers of well-known polynomial sequences such as Fibonacci, Lucas, Pell, Jacobsthal, and Chebyshev polynomials. Finally, we point out some interesting divisibility properties between polynomials arising from our results.

scholarly journals Some Identities Involving the Derivative of the First Kind Chebyshev Polynomials

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Tingting Wang ◽  
Han Zhang
Keyword(s):  
Open Problem ◽  
Chebyshev Polynomials ◽  
Combinatorial Method ◽  
Power Sums

We use the combinatorial method and algebraic manipulations to obtain several interesting identities involving the power sums of the derivative of the first kind Chebyshev polynomials. This solved an open problem proposed by Li (2015).

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

2017 ◽  
Vol 2017 ◽  
pp. 1-6
Author(s):  
Lan Zhang ◽  
Wenpeng Zhang
Keyword(s):  
Chebyshev Polynomials ◽  
Fibonacci Numbers ◽  
Mathematical Induction ◽  
Lucas Numbers ◽  
Sums Of Powers

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.

Divisibility Properties of Graded Domains

1982 ◽  
Vol 34 (1) ◽  
pp. 196-215 ◽  
Author(s):  
D. D. Anderson ◽  
David F. Anderson
Keyword(s):  
Integral Domain ◽  
Homogeneous Element ◽  
Carry Over ◽  
Divisibility Properties ◽  
Krull Domains

Let R = ⊕α∊гRα be an integral domain graded by an arbitrary torsionless grading monoid Γ. In this paper we consider to what extent conditions on the homogeneous elements or ideals of R carry over to all elements or ideals of R. For example, in Section 3 we show that if each pair of nonzero homogeneous elements of R has a GCD, then R is a GCD-domain. This paper originated with the question of when a graded UFD (every homogeneous element is a product of principal primes) is a UFD. If R is Z+ or Z-graded, it is known that a graded UFD is actually a UFD, while in general this is not the case. In Section 3 we consider graded GCD-domains, in Section 4 graded UFD's, in Section 5 graded Krull domains, and in Section 6 graded π-domains.

scholarly journals Factors of alternating sums of powers of q -Narayana numbers

2017 ◽  
Vol 177 ◽  
pp. 37-42 ◽  
Author(s):  
Victor J.W. Guo ◽  
Qiang-Qiang Jiang
Keyword(s):  
Sums Of Powers ◽  
Alternating Sums ◽  
Narayana Numbers

On the Security of Public-Key Algorithms Based on Chebyshev Polynomials over the Finite Field $Z_N$

2010 ◽  
Vol 59 (10) ◽  
pp. 1392-1401 ◽  
Author(s):  
Xiaofeng Liao ◽  
Fei Chen ◽  
Kwok-wo Wong
Keyword(s):  
Finite Field ◽  
Chebyshev Polynomials ◽  
Public Key
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