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Notes on Number Theory and Discrete Mathematics, Volume 28; https://doi.org/10.7546/nntdm.2022.28.3.533-541

Abstract:
For a given prime p ≥ 5, let ℤ_p denote the set of rational p-integers (those rational numbers whose denominator is not divisible by p). In this paper, we establish some congruences modulo a prime power p5 on the hyper-sums of powers of integers in terms of Fermat quotient, Wolstenholme quotient, Bernoulli and Euler numbers.
Notes on Number Theory and Discrete Mathematics, Volume 28; https://doi.org/10.7546/nntdm.2022.28.3.525-532

Abstract:
We continue the study from [1], by studying equations of type $\psi(n) = \dfrac{k+1}{k} \cdot \ n+a,$ $a\in \{0, 1, 2, 3\},$ and $\varphi(n) = \dfrac{k-1}{k} \cdot \ n-a,$ $a\in \{0, 1, 2, 3\}$ for $k > 1,$ where $\psi(n)$ and $\varphi(n)$ denote the Dedekind, respectively Euler's, arithmetical functions.
Notes on Number Theory and Discrete Mathematics, Volume 28; https://doi.org/10.7546/nntdm.2022.28.3.500-506

Abstract:
In this paper, we study asymptotic behaviour of the sum $\sum_{n\leq N}{f}\Big(\lfloor n^c \rfloor\Big),$ where $f(n)=\sum_{d^2\mid n}g(d)$ under three different types of assumptions on $g$ and $1& < c < 2$.
Anthony G. Shannon,
Notes on Number Theory and Discrete Mathematics, Volume 28; https://doi.org/10.7546/nntdm.2022.28.3.507-516

Abstract:
This paper builds on Roettger and Williams’ extensions of the primordial Lucas sequence to consider some relations among difference equations of different orders. This paper utilises some of their second and third order recurrence relations to provide an excursion through basic second order sequences and related third order recurrence relations with a variety of numerical illustrations which demonstrate that mathematical notation is a tool of thought.
Notes on Number Theory and Discrete Mathematics, Volume 28; https://doi.org/10.7546/nntdm.2022.28.3.491-499

Abstract:
In this paper, B-Tribonacci polynomials which are extensions of Fibonacci polynomials are defined. Some identities relating B-Tribonacci polynomials and their derivatives are established.
Notes on Number Theory and Discrete Mathematics, Volume 28; https://doi.org/10.7546/nntdm.2022.28.3.477-490

Abstract:
In this paper, we define and investigate the generalized Pisano sequences and we deal with, in detail, two special cases, namely, Pisano and Pisano–Lucas sequences. We present Binet’s formulas, generating functions and Simson’s formulas for these sequences. Moreover, we give some identities and matrices associated with these sequences. Furthermore, we show that there are close relations between Pisano and Pisano–Lucas numbers and modified Oresme, Oresme–Lucas and Oresme numbers.
Notes on Number Theory and Discrete Mathematics, Volume 28; https://doi.org/10.7546/nntdm.2022.28.3.466-476

Abstract:
In this paper, we derive some important identities involving k-Jacobsthal and k-Jacobsthal–Lucas numbers. Moreover, we use multinomial theorem to obtain distinct binomial sums of k-Jacobsthal and k-Jacobsthal–Lucas numbers.
Notes on Number Theory and Discrete Mathematics, Volume 28; https://doi.org/10.7546/nntdm.2022.28.3.458-465

Abstract:
In this study, we introduce the complex Leonardo numbers and give some of their properties including Binet formula, generating function, Cassini and d’Ocagne’s identities. Also, we calculate summation formulas for complex Leonardo numbers involving complex Fibonacci and Lucas numbers.
, World Intelligence Network Spiqr Society,
Notes on Number Theory and Discrete Mathematics, Volume 28; https://doi.org/10.7546/nntdm.2022.28.3.441-457

Abstract:
In the present paper we provide a formula that allows to compute the number of stable digits of any integer tetration base a \in {\mathbb N}_0. The number of stable digits, at the given height of the power tower, indicates how many of the last digits of the (generic) tetration are frozen. Our formula is exact for every tetration base which is not coprime to 10, although a maximum gap equal to V(a)+1 digits (where V(a) denotes the constant congruence speed of a) can occur, in the worst-case scenario, between the upper and lower bound. In addition, for every a>1 which is not a multiple of 10, we show that V(a) corresponds to the 2-adic or 5-adic valuation of a-1 or a+1, or even to the 5-adic order of a^2+1, depending on the congruence class of a modulo 20.
Sunanta Srisopha, King Mongkut’s Institute of Technology Ladkrabang, Teerapat Srichan, , Kasetsart University
Notes on Number Theory and Discrete Mathematics, Volume 28; https://doi.org/10.7546/nntdm.2022.28.3.435-440

Abstract:
Let P be a finite set of prime numbers. By using an elementary method, the proportion of all r-free numbers which are divisible by at least one element in P is studied.
, Tampere University
Notes on Number Theory and Discrete Mathematics, Volume 28; https://doi.org/10.7546/nntdm.2022.28.3.411-434

Abstract:
A divisor d of a positive integer n is called a unitary divisor if \gcd(d, n/d)=1; and d is called a bi-unitary divisor of n if the greatest common unitary divisor of d and n/d is unity. The concept of a bi-unitary divisor is due to D. Surynarayana (1972). Let \sigma^{**}(n) denote the sum of the bi-unitary divisors of n. A positive integer n is called a bi-unitary multiperfect number if \sigma^{**}(n)=kn for some k\geq 3. For k=3 we obtain the bi-unitary triperfect numbers. Peter Hagis (1987) proved that there are no odd bi-unitary multiperfect numbers. The present paper is part IV(c) in a series of papers on even bi-unitary multiperfect numbers. In parts I, II and III we determined all bi-unitary triperfect numbers of the form n=2^{a}u, where 1\leq a \leq 6 and u is odd. In part V we fixed the case a=8. The case a=7 is more difficult. In Parts IV(a-b) we solved partly this case, and in the present paper (Part IV(c)) we continue the study of the same case (a=7).
, Beykent University, , , Istanbul Gelisim University, Ankara Hacı Bayram Veli University
Notes on Number Theory and Discrete Mathematics, Volume 28; https://doi.org/10.7546/nntdm.2022.28.3.399-410

Abstract:
This paper focuses on a specially constructed matrix whose entries are harmonic Fibonacci numbers and considers its Hadamard exponential matrix. A lot of admiring algebraic properties are presented for both of them. Some of them are determinant, inverse in usual and in the Hadamard sense, permanents, some norms, etc. Additionally, a MATLAB-R2016a code is given to facilitate the calculations and to further enrich the content.
, Sainkupar Mn Mawiong
Notes on Number Theory and Discrete Mathematics, Volume 28; https://doi.org/10.7546/nntdm.2022.28.3.383-398

Abstract:
The Laplacian-energy-like invariant of a finite simple graph is the sum of square roots of all its Laplacian eigenvalues and the incidence energy is the sum of square roots of all its signless Laplacian eigenvalues. In this paper, we give the bounds on the Laplacian-energy-like invariant and incidence energy of the corona and edge corona of two graphs. We also observe that the bounds on the Laplacian-energy-like invariant and incidence energy of the corona and edge corona are sharp when the graph is the corona or edge corona of two complete graphs.
Notes on Number Theory and Discrete Mathematics, Volume 28; https://doi.org/10.7546/nntdm.2022.28.2.350-375

Abstract:
This paper considers properties of a theorem of Ramanujan to develop properties and algorithms related to cubic equations. The Ramanujan cubics are related to the Cardano cubics and Padovan recurrence relations. These generate cubic identities related to heptagonal triangles and third order recurrence relations, as well as an algorithm for finding the real root of the relevant Ramanujan cubic equation. The algorithm is applied to, and analyzed for, some of the earlier examples in the paper.
, Babeș-Bolyai University,
Notes on Number Theory and Discrete Mathematics, Volume 28; https://doi.org/10.7546/nntdm.2022.28.2.376-379

Abstract:
By using the results and methods of [1], we will study the equation \varphi(n) + d(n) = \frac{n}{2} and the related inequalities. The equation \varphi(n) + d^2(n)=2n will be solved, too.
, Zian Achour University of Djelfa,
Notes on Number Theory and Discrete Mathematics, Volume 28; https://doi.org/10.7546/nntdm.2022.28.2.234-239

Abstract:
In this paper, we use the properties of the classical umbral calculus to determine sequences related to the Bell numbers and having periods divide (formula).
Notes on Number Theory and Discrete Mathematics, Volume 28; https://doi.org/10.7546/nntdm.2022.28.2.200-233

Abstract:
{\bf } Multiple zeta values have become of great interest due to their numerous applications in mathematics and physics. In this article, we present a generalization, which we will refer to as multiple sums, where the reciprocals are replaced with arbitrary sequences. We develop formulae to help with manipulating such sums. We develop variation formulae that express the variation of multiple sums in terms of lower order multiple sums. Additionally, we derive a set of partition identities that we use to prove a reduction theorem that expresses multiple sums as a combination of simple sums. We present a variety of applications including applications concerning polynomials and MZVs such as generating functions and expressions for $\zeta(\{2p\}_m)$ and $\zeta^\star(\{2p\}_m)$. Finally, we establish the connection between multiple sums and a type of sums called recurrent sums. By exploiting this connection, we provide additional partition identities for odd and even partitions.
Notes on Number Theory and Discrete Mathematics, Volume 28; https://doi.org/10.7546/nntdm.2022.28.2.167-199

Abstract:
Multiple zeta star values have become a central concept in number theory with a wide variety of applications. In this article, we propose a generalization, which we will refer to as recurrent sums, where the reciprocals are replaced by arbitrary sequences. We introduce a toolbox of formulas for the manipulation of such sums. We begin by developing variation formulas that allow the variation of a recurrent sum of order $m$ to be expressed in terms of lower order recurrent sums. We then proceed to derive theorems (which we will call inversion formulas) which show how to interchange the order of summation in a multitude of ways. Later, we introduce a set of new partition identities in order to then prove a reduction theorem which permits the expression of a recurrent sum in terms of a combination of non-recurrent sums. Finally, we use these theorems to derive new results for multiple zeta star values and recurrent sums of powers.
, Erzincan Binali Yıldırım University,
Notes on Number Theory and Discrete Mathematics, Volume 28; https://doi.org/10.7546/nntdm.2022.28.2.318-330

Abstract:
In this work, we investigate the hyperbolic k-Jacobsthal and k-Jacobsthal–Lucas octonions. We give Binet’s Formula, Cassini’s identity, Catalan’s identity, d’Ocagne identity, generating functions of the hyperbolic k-Jacobsthal and k-Jacobsthal–Lucas octonions. Also, we present many properties of these octonions.
Krassimir T. Atanassov
Notes on Number Theory and Discrete Mathematics, Volume 28; https://doi.org/10.7546/nntdm.2022.28.2.331-338

Abstract:
A new scheme of 2-Fibonacci sequences is introduced and the explicit formulas for its n-th members are given. For difference of all previous sequences from Fibonacci type, the present 2-Fibonacci sequences are obtained by a new way. It is proved that the new sequences have bases with 48 elements about function 𝜑 and modulo 9.
Notes on Number Theory and Discrete Mathematics, Volume 28; https://doi.org/10.7546/nntdm.2022.28.2.339-349

Abstract:
In this paper, we define the Hadamard-type k-step Pell sequence by using the Hadamard-type product of characteristic polynomials of the Pell sequence and the k-step Pell sequence. Also, we derive the generating matrices for these sequences, and then we obtain relationships between the Hadamard-type k-step Pell sequences and these generating matrices. Furthermore, we produce the Binet formula for the Hadamard-type k-step Pell numbers for the case that k is odd integers and k ≥ 3. Finally, we derive some properties of the Hadamard-type k-step Pell sequences such as the combinatorial representation, the generating function, and the exponential representation by using its generating matrix.
, , Professional Master Degree Program In Mathematics In National Network – Profmat
Notes on Number Theory and Discrete Mathematics, Volume 28; https://doi.org/10.7546/nntdm.2022.28.2.302-317

Abstract:
The Navarrete–Orellana Conjecture states that “given a large prime number a sequence is generated, in such a way that all odd prime numbers, except the given prime, are fixed points of that sequence”. In this work, we formulated a theorem that partially confirms the veracity of this conjecture, more specifically, all prime numbers of a given line segment are fixed points of this sequence.
Eiji Miyanohara, Japan Tokyo
Notes on Number Theory and Discrete Mathematics, Volume 28; https://doi.org/10.7546/nntdm.2022.28.2.159-166

Abstract:
In 1929, Mahler proved that the real number generated by Thue–Morse sequence is transcendental. Later, Adamczewski and Bugeaud gave a different proof of the transcendence of this number using a combinatorial transcendence criterion. Moreover, Kumar and Meher gave the generalization of the combinatorial transcendence criterion under the subspace Lang conjecture. In this paper, we prove under the subspace Lang conjecture that the real number generated by Thue–Morse along squares is transcendental by using the combinatorial transcendence criterion of Kumar and Meher.
Notes on Number Theory and Discrete Mathematics, Volume 28; https://doi.org/10.7546/nntdm.2022.28.2.286-301

Abstract:
In this study, we deal with the existence of perfect powers which are sum and difference of two balancing numbers. Moreover, as a generalization we explore the perfect squares which are sum and difference of two balancing-like numbers, where balancing-like sequence is defined recursively as $G_{n+1}=AG_n-G_{n-1}$ with initial terms $G_0=0,G_1=1$ for $A \geq 3$.
Notes on Number Theory and Discrete Mathematics, Volume 28; https://doi.org/10.7546/nntdm.2022.28.2.281-285

Abstract:
We study equations of type $\sigma(n) = \dfrac{k+1}{k} \cdot n+a,$ where $a\in \{0, 1, 2, 3\},$ where $k$ and $n$ are positive integers, while $\sigma(n)$ denotes the sum of divisors of $n.$
, Ain Shams University
Notes on Number Theory and Discrete Mathematics, Volume 28; https://doi.org/10.7546/nntdm.2022.28.2.276-280

Abstract:
Given a positive integer $x$, an addition chain for $x$ is an increasing sequence of positive integers $1=c_0,c_1, \ldots , c_n=x$ such that for each $1\leq k\leq n,$ $c_k=c_i+c_j$ for some $0\leq i\leq j\leq k-1$. In 1937, Scholz conjectured that for each positive integer $x$, $\ell(2^x-1) \leq \ell(x)+ x-1,$ where $\ell(x)$ denotes the minimal length of an addition chain for $x.$ In 1993, Aiello and Subbarao stated the apparently stronger conjecture that there is an addition chain for $2^x-1$ with length equals to $\ell(x)+x-1 .$ We note that the Aiello–Subbarao conjecture is not stronger than the Scholz (also called the Scholz–Brauer) conjecture.
Notes on Number Theory and Discrete Mathematics, Volume 28; https://doi.org/10.7546/nntdm.2022.28.2.252-260

Abstract:
In this study, we take the generalized Fibonacci sequence \{u_{n}\} as u_{0}=0,u_{1}=1 and \ u_{n}=ru_{n-1}+u_{n-2} for n>1, where r is a non-zero integer. Based on Halton’s paper in [4], we derive three interrelated functions involving the terms of generalized Fibonacci sequence \{u_{n}\}. Using these three functions we introduce a simple approach to obtain a lot of identities, binomial sums and alternate binomial sums involving the terms of generalized Fibonacci sequence \{u_{n}\}.
, Yildiz Technical University
Notes on Number Theory and Discrete Mathematics, Volume 28; https://doi.org/10.7546/nntdm.2022.28.2.261-275

Abstract:
In the paper, we define the q-Fibonacci bicomplex numbers and the q-Lucas bicomplex numbers, respectively. Then, we give some algebraic properties of the q-Fibonacci bicomplex numbers and the q-Lucas bicomplex numbers.
B. M. Phong, R. B. Szeidl
Notes on Number Theory and Discrete Mathematics, Volume 28; https://doi.org/10.7546/nntdm.2022.28.2.240-251

Abstract:
We give all solutions $f:\Bbb N \to \Bbb C$ of the functional equation $$f(n^2-Dnm+m^2)=f^2(n)-Df(n)f(m)+f^2(m),$$ where $D\in\{1,2\}$.
Notes on Number Theory and Discrete Mathematics, Volume 28; https://doi.org/10.7546/nntdm.2022.28.2.147-158

Abstract:
We describe and compare several novel sieve-like methods. They assign values of several functions (i.e., the prime omega functions ω and Ω and the divisor function d) to each natural number in the considered range of integer numbers. We prove that in some cases the algorithms presented have a relatively small computational complexity. A more detailed output is indeed obtained with respect to the original Sieve of Eratosthenes.
Notes on Number Theory and Discrete Mathematics, Volume 28; https://doi.org/10.7546/nntdm.2022.28.1.129-142

Abstract:
We consider the extension of generalized arithmetic triangle to negative values of rows and we describe the recurrence relation associated to the sum of diagonal elements laying along finite rays. We also give the corresponding generating function. We conclude by an application to Fibonacci numbers and Morgan-Voyce polynomials with negative subscripts.
Notes on Number Theory and Discrete Mathematics, Volume 28; https://doi.org/10.7546/nntdm.2022.28.1.143-146

Abstract:
Two new combined 3-Fibonacci sequences are introduced and the explicit formulae for their n-th members are given.
Notes on Number Theory and Discrete Mathematics, Volume 28; https://doi.org/10.7546/nntdm.2022.28.1.124-128

Abstract:
As a continuation of [6], we deduce some inequalities of a new type for the prime counting function π(x).
Notes on Number Theory and Discrete Mathematics, Volume 28; https://doi.org/10.7546/nntdm.2022.28.1.115-123

Abstract:
Given the purpose of mathematical evolution of Leonardo's sequence, we have the prospect of introducing complex polynomials, bivariate polynomials and bivariate polynomials around these numbers. Thus, this article portrays in detail the insertion of the variable x, y and the imaginary unit i in the sequence of Leonardo. Nevertheless, the mathematical results from this process of complexification of these numbers are studied, correlating the mathematical evolution of that sequence.
Notes on Number Theory and Discrete Mathematics, Volume 28; https://doi.org/10.7546/nntdm.2022.28.1.100-108

Abstract:
Let $n$ and $k$ be two positive integers and let $A$ be a set of positive integers. We define $t_A(n,k)$ to be the number of partitions of $n$ with exactly $k$ sizes and parts in $A$. As an implication of a variant of Newton's product-sum identities we present a generating function for $t_A(n,k)$. Subsequently, we obtain a recurrence relation for $t_A(n,k)$ and a divisor-sum expression for $t_A(n,2)$. Also, we present a bijective proof for the latter expression.
Notes on Number Theory and Discrete Mathematics, Volume 28; https://doi.org/10.7546/nntdm.2022.28.1.109-114

Abstract:
This note considers some real and complex extensions and generalizations of the Leonardo sequence, which is embedded within each of these two types of intriguing sequences, intriguing because there are still some unanswered questions. The connections between inhomogeneous and homogeneous forms are used as examples of a possible reason that the Leonardo sequences have been, in a sense, historically neglected.
Notes on Number Theory and Discrete Mathematics, Volume 28; https://doi.org/10.7546/nntdm.2022.28.1.92-99

Abstract:
In this paper, we establish some sums involving generalized harmonic and Daehee numbers which are derived from the generating functions. For example, for $n, r\geq 1,$ \begin{eqnarray*} \sum_{i=0}^{n}H\left( i,r-1,\alpha \right) H_{n-i}^{r}\left( \alpha \right) &=&\sum_{l_{1}+l_{2}+ \cdots +l_{r+1}=n}H_{l_{1}}(\alpha )H_{l_{2}}(\alpha ) \cdots H_{l_{r+1}}(\alpha ). \end{eqnarray*}
, Hanoi University of Science and Technology
Notes on Number Theory and Discrete Mathematics, Volume 28; https://doi.org/10.7546/nntdm.2022.28.1.75-80

Abstract:
We show that if a is a positive integer such that for each positive integer n, a+n^2 can be expressed x^2+y^2, where x,y\in \mathbb{Z}, then a is a square number. A similar theorem also holds if a+n^2 and x^2+y^2 are replaced by a+2n^2 and x^2+2y^2, respectively.
Notes on Number Theory and Discrete Mathematics, Volume 28; https://doi.org/10.7546/nntdm.2022.28.1.64-74

Abstract:
Recently companion sequences of r-Fibonacci sequence were defined. The aim of this paper is to give some determinantal and permanental representations of these sequences via Hessenberg matrices. Several representations of classical sequences and polynomials are established. We conclude by using our representations to give n consecutive terms of companion sequences simultaneously.
Notes on Number Theory and Discrete Mathematics, Volume 28; https://doi.org/10.7546/nntdm.2022.28.1.41-47

Abstract:
The amplitude of Motzkin paths was recently introduced, which is basically twice the height. We analyze this parameter using generating functions.
Notes on Number Theory and Discrete Mathematics, Volume 28; https://doi.org/10.7546/nntdm.2022.28.1.48-63

Abstract:
Consider a sequence of numbers x_n \in \mathbb{Z_+} defined by x_{n+1}= \frac{x_n}{2} if x_n is even, and x_{n+1}= \frac{x_n+2x_{n-1}+q}{2} if x_n is odd. A 1-cycle is a periodic sequence with one transition from odd to even numbers. We prove theoretical and computational results for the existence of 1-cycles, and discuss a generalization to more complex cycles.
, Konya Technical University, , Purdue University Northwest
Notes on Number Theory and Discrete Mathematics, Volume 28; https://doi.org/10.7546/nntdm.2022.28.1.21-25

Abstract:
Let $b\in \left\{ 2,3, \ldots,9\right\}.$ In this paper, we show that the solutions of the equation $\left( x\right) _{b}=m! $ are $\left( 11\right) _{5}=3!, \left( 33\right) _{7}=\left( 44\right)_{5}=4!$, where $\left( x\right) _{b}$ has at least two digits.
Notes on Number Theory and Discrete Mathematics, Volume 28; https://doi.org/10.7546/nntdm.2022.28.1.26-40

Abstract:
In this study, the hybrid-hyperbolic numbers are introduced. This number system is a more general form of the hybrid number system, which is an interesting number system, as well as a number system that includes multicomponent number systems (i.e., complex-hyperbolic, dual-hyperbolic and bihyperbolic numbers). In this paper, we give algebraic properties of hybrid-hyperbolic numbers. In addition, 2 × 2 and 4 × 4 hyperbolic matrix representations of hybrid-hyperbolic numbers are given and some properties of them are examined.
Correction
, Lulea University of Technology,
Notes on Number Theory and Discrete Mathematics, Volume 28; https://doi.org/10.7546/nntdm.2022.28.1.20

Abstract:
Corrigendum to “On the dimension of an Abelian group” [Notes on Number Theory and Discrete Mathematics, 2021, Volume 27, Number 4, Pages 267—275]
, Rajamangala University of Technology, , Kitsana Charoenchaianan
Notes on Number Theory and Discrete Mathematics, Volume 28; https://doi.org/10.7546/nntdm.2022.28.1.9-19

Abstract:
In this paper, we first introduce the generalization of the Vieta–Jacobsthal polynomial, which is called the Vieta–Jacobsthal-like polynomial. After that, we give the generating function, the Binet formula, and some well-known identities for this polynomial. Finally, we also present the relation between this polynomial and the previously famous Vieta polynomials.
, Netaji Subhas University of Technology, Sangeeta Chaudhary, , Jawaharlal Nehru University, University of Monastir
Notes on Number Theory and Discrete Mathematics, Volume 28; https://doi.org/10.7546/nntdm.2022.28.1.1-8

Abstract:
The authors establish a set of fourteen character formulas in terms of R_{\beta} and R_{m} functions. Folsom [6] studied character formulas and Chaudhary [5] expressed those formulas in terms of continued fraction identities. Andrews et al. [2] introduced multivariate R-functions, which are further classified as R_{\alpha}, R_{\beta}, and R_{m} (for m = 1, 2, 3, …) functions by Srivastava et al. [10].
, Nevşehir Hacı Bektaş Veli University
Notes on Number Theory and Discrete Mathematics, Volume 27; https://doi.org/10.7546/nntdm.2021.27.4.207-218

Abstract:
In this study, we investigate the connection between second order recurrence matrix and several combinatorial matrices such as generalized r-eliminated Pascal matrix, Stirling matrix of the first and of the second kind matrices. We give factorizations and inverse factorizations of these matrices by virtue of the second order recurrence matrix. Moreover, we derive several combinatorial identities which are more general results of some earlier works.
, Obafemi Awolowo University,
Notes on Number Theory and Discrete Mathematics, Volume 27; https://doi.org/10.7546/nntdm.2021.27.4.95-103

Abstract:
We derive new infinite series involving Fibonacci numbers and Riemann zeta numbers. The calculations are facilitated by evaluating linear combinations of polygamma functions of the same order at certain arguments.
, Pamukkale University, , Kafkas University
Notes on Number Theory and Discrete Mathematics, Volume 27; https://doi.org/10.7546/nntdm.2021.27.4.236-244

Abstract:
In this study, we have defined Fibonacci quaternion matrix and investigated its powers. We have also derived some important and useful identities such as Cassini’s identity using this new matrix.
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