Related papers: Exponent Lifting Property of Integer Sequences
We define lifting properties for universal algebras, which we study in this general context and then particularize to various such properties in certain classes of algebras. Next we focus on residuated lattices, in which we investigate…
We say that an arithmetical function $S:\mathbb{N}\rightarrow\mathbb{Z}$ has Lucas property if for any prime $p$, \begin{equation*} S(n)\equiv S(n_{0})S(n_{1})\ldots S(n_{r})\pmod p, \end{equation*} where $n=\sum_{i=0}^{r}n_{i}p^{i}$, with…
We explore the lifting question in the context of cut-generating functions. Most of the prior literature on this question focuses on cut-generating functions that have the unique lifting property. We develop a general theory for…
In this paper, we define Tribonacci and Tribonacci-Lucas matrix sequences and investigate their properties.
We present numerous interesting, mostly new, results involving the $n$-step Fibonacci numbers and $n$-step Lucas numbers and a generalization. Properties considered include recurrence relations, summation identities, including binomial and…
In this paper, we investigate the convergence exponent of Pierce expansion digit sequences. We explore some basic properties of the convergence exponent as a real-valued function defined on the closed unit interval, as well as those of the…
We give several simple and easy complements to our recent paper on $C^*$-algebras with the lifting property (LP in short). In particular we observe that the local lifting property (LLP in short) associated to the class of max-contractions…
We study formal power series which can be interpreted as interpolations of Fibonacci and Lucas polynomials with even (or odd) indices.
In this paper we determine some properties of Fibonacci octonions. Also, we introduce the generalized Fibonacci-Lucas octonions and we investigate some properties of these elements.
The purpose of this memoir is to discuss two very interesting properties of integer sequences. One is the law of apparition and the other is the law of repetition. Both have been extensively studied by mathematicians such as Ward, Lucas,…
For the Lucas sequence $\{U_{k}(P,Q)\}$ we discuss the identities such as the well-known Fibonacci identities. We also propose a method for obtaining identities involving recurrence sequences. With the help of which we find an interpolating…
In this paper we study the sets of integers which are $n$-th terms of Lucas sequences. We establish lower- and upper bounds for the size of these sets. These bounds are sharp for $n$ sufficiently large. We also develop bounds on the growth…
The objective of this manuscript is to offer explicit expressions for diverse categories of infinite series incorporating the Fibonacci (Lucas) sequence and the Riemann zeta function. In demonstrating our findings, we will utilize…
In this paper, we provide properties and applications of some special integer sequences. We generalize and give some properties of Pisano period. Moreover, we provide a new application in Cryptography and applications of some quaternion…
The classical Fibonacci sequence is known to exhibit many fascinating properties. In this paper, we explore the Fibonacci sequence and integer sequences generated by second order linear recurrence relations with positive integer…
The purpose of this article is to present closed forms for various types of infinite series involving Fibonacci (Lucas) numbers and the Riemann zeta function at integer arguments.
The purpose of this paper is to introduce the space of geometric sequences that are strongly summable with respect to an Orlicz function and the Fibonacci difference sequences.Also some topological properties and inclusion relations between…
In this paper we study the Fibonacci numbers and derive some interesting properties and recurrence relations. We prove some charecterizations for $F_p$, where $p$ is a prime of a certain type. We also define period of a Fibonacci sequence…
This paper is the continuation of \cite{htl}, where we deal with Lucas sequences. Here we study integers represented by integer sequences which satisfy binary recursive relations. In case of non-degenerate sequences we give bounds for the…
In this paper we discuss near-perfect numbers of various forms. In particular, we study the existence of near-perfect numbers in the Fibonacci and Lucas sequences, near-perfect values taken by integer polynomials and repdigit near-perfect…