Results 41 to 50 of about 1,598,417 (209)

Cryptography using Fibonacci-Mersenne and Fibonacci-balancing p-sequences with a self-invertible matrix and the Affine-Hill cipher [PDF]

Notes on Number Theory and Discrete Mathematics
In this paper, we define two new sequences using the Fibonacci p-numbers, the generalized Mersenne numbers, and m-balancing numbers. These sequences are obtained from the corresponding characteristic polynomials.
Elahe Mehraban, T. Aaron Gulliver, Ömür Deveci, Evren Hincal   +3 more
doaj   +1 more source

Higher-Order Mersenne Numbers: New Sequences, Algebraic Properties, and Binomial Transforms

Mathematical sciences and applications e-notes
This article introduces and investigates a new integer sequence, termed the higher-order Mersenne sequence, defined in analogy with higher-order Fibonacci numbers and closely related to classical Mersenne numbers.
K. Prasad, Munesh Kumari, Rabiranjan Mohanta, H. Mahato   +3 more
semanticscholar   +1 more source

Mersenne k-Fibonacci numbers

Glasnik matematički, 2016
For an integer k≥ 2, let (Fn(k))n be the k-Fibonacci sequence which starts with 0,...,0,1 (k terms) and each term afterwards is the sum of the k preceding terms. In this paper, we find all k-Fibonacci numbers which are Mersenne numbers, i.e., k-Fibonacci numbers that are equal to 1 less than a power of 2.
Bravo, Jhon J., Gómez, Carlos A.
openaire   +3 more sources

Boolean Hypercubes: The Origin of a Tagged Recursive Logic and the Limits of Artificial Intelligence

Universal Journal of Mathematics and Applications, 2021
Boolean and logical hypercubes are discussed as providers of tags to logical object sets, transforming them into logical tagged sets, a generalization of fuzzy sets.
Ramon Carbó-dorca
doaj   +1 more source

Generalization of Gaussian Mersenne numbers and their new families

Mathematics and Computer Science
In this article, we present the generalized Gaussian Mersenne numbers with arbitrary initial values and discuss two particular cases, namely, Gaussian Mersenne and Gaussian Mersenne-Lucas numbers.
Munesh Kumari, K. Prasad, J. Tanti
semanticscholar   +1 more source

EXPONENTIAL AND CHARACTER SUMS WITH MERSENNE NUMBERS [PDF]

Journal of the Australian Mathematical Society, 2012
AbstractWe give new bounds on sums of the form ∑ n≤NΛ(n)exp (2πiagn/m) and ∑ n≤NΛ(n)χ(gn+a), where Λ is the von Mangoldt function, m is a natural number, a and g are integers coprime to m, and χ is a multiplicative character modulo m. In particular, our results yield bounds on the sums ∑ p≤Nexp (2πiaMp/m) and ∑ p≤Nχ(Mp) with Mersenne numbers Mp=2p−1 ...
Banks, William D., Friedlander, John B., Garaev, Moubariz Z., Shparlinski, Igor E.   +3 more
openaire   +1 more source

Bipartite Graphs Associated with Pell, Mersenne and Perrin Numbers

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2019
In this paper, we consider the relationships between the numbers of perfect matchings (1-factors) of bipartite graphs and Pell, Mersenne and Perrin Numbers.
Öteleş Ahmet
doaj   +1 more source

Affine–Hill cipher from Hadamard-type Fibonacci–Mersenne and Fibonacci-balancing p-sequences [PDF]

Notes on Number Theory and Discrete Mathematics
In this paper, we define two new sequences using the generalized Mersenne numbers, Fibonacci p-numbers, and m-balancing numbers. These sequences are constructed using the Hadamard-type product of their characteristic polynomials.
Elahe Mehraban, T. Aaron Gulliver, Evren Hincal   +2 more
doaj   +1 more source

Mersenne-Horadam identities using generating functions

Karpatsʹkì Matematičnì Publìkacìï, 2020
The main object of the present paper is to reveal connections between Mersenne numbers $M_n=2^n-1$ and generalized Fibonacci (i.e., Horadam) numbers $w_n$ defined by a second order linear recurrence $w_n=pw_{n-1}+qw_{n-2}$, $n\geq 2$, with $w_0=a$ and ...
R. Frontczak, T.P. Goy
doaj   +1 more source

An Encoding –Decoding Algorithm Based on k-Fermat and k-Mersenne Numbers

Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi
In this study, we present an encoding/decoding algorithm using k-Fermat and k-Mersenne numbers. We use Fermat Q-matrices and Mersenne R-matrices, the terms of these matrices are composed of k-Fermat and k-Mersenne numbers, respectively, and look like ...
Engin Eser, Bahar Kuloǧlu, E. Özkan
semanticscholar   +1 more source