Results 51 to 60 of about 1,598,417 (209)

On Generalized p-Mersenne Numbers

Earthline Journal of Mathematical Sciences, 2021
In this paper, we introduce the generalized p-Mersenne sequence and deal with, in detail, two special cases, namely, p-Mersenne and p-Mersenne-Lucas-sequences. We present Binet’s formulas, generating functions, Simson formulas, and the summation formulas
Y. Soykan
semanticscholar   +1 more source

On the square-freeness of Fermat and Mersenne numbers [PDF]

Pacific Journal of Mathematics, 1967
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Warren, Leroy J., Bray, Henry G.
openaire   +3 more sources

The First Study of Mersenne--Leonardo Sequence

Communications in Advanced Mathematical Sciences
In this study, we introduce a new class of numbers, referred to as Modified Mersenne--Leonardo numbers. The aim of this paper is to define the Modified Mersenne--Leonardo sequence and investigate some of its properties, including the recurrence relation,
Paula Maria Machado Cruz Catarino, Eudes Antonio Costa   +1 more
doaj   +1 more source

Improved cryptanalysis of the AJPS Mersenne based cryptosystem

Journal of Mathematical Cryptology, 2020
At Crypto 2018, Aggarwal, Joux, Prakash and Santha (AJPS) described a new public-key encryption scheme based on Mersenne numbers. Shortly after the publication of the cryptosystem, Beunardeau et al. described an attack with complexity 𝓞(22h).
Coron Jean-Sébastien, Gini Agnese
doaj   +1 more source

Boolean Hypercubes, Classification of Natural Numbers, and the Collatz Conjecture

Journal of Mathematical Sciences and Modelling, 2022
Using simple arguments derived from the Boolean hypercube configuration, the structure of natural spaces, and the recursive exponential generation of the set of natural numbers, a linear classification of the natural numbers is presented.
Ramon Carbó Dorca, Carlos Perelman
doaj   +1 more source

Note on a Mersenne number [PDF]

Bulletin of the American Mathematical Society, 1934
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +2 more sources

Generalized Mersenne numbers of the form cx²

Annales Mathematicae et Informaticae, 2022
Generalized Mersenne numbers are defined as 𝑀 𝑝,𝑛 = 𝑝 𝑛 − 𝑝 +1 , where 𝑝 is a prime and 𝑛 is a positive integer. Here, we prove that for each pair ( 𝑐, 𝑝 ) with 𝑐 ≥ 1 an integer, there is at most one 𝑀 𝑝,𝑛 of the form 𝑐𝑥 2 with a few exceptions.
Azizul Hoque
semanticscholar   +1 more source

Rocking and Rolling of Rigid Polygons Under Seismic Excitation

Earthquake Engineering &Structural Dynamics, EarlyView.
ABSTRACT We present an event driven analytical framework for rigid cyclic polygons subjected to horizontal ground excitation in which uplift, impact, and successive pivot switching are treated within a unified non‐smooth dynamical description. Rolling is defined as a sequence of energetically admissible transitions between neighbouring vertices tied to
Atif Rasheed, Christian Málaga‐Chuquitaype   +1 more
wiley   +1 more source

Generalized Commutative Mersenne and Mersenne–Lucas Quaternion Polynomials

Annales Mathematicae Silesianae
Generalized commutative quaternions generalize elliptic, parabolic and hyperbolic quaternions, bicomplex numbers, complex hyperbolic numbers and hyperbolic complex numbers. In this paper, we use the Mersenne numbers and polynomials in the theory of these
Bród Dorota, Szynal-Liana Anetta, Liana Mirosław   +2 more
doaj   +1 more source

On Generalized Mersenne Numbers and Extended Fermat Numbers

European Journal of Pure and Applied Mathematics
In this paper, we study a generalization of Mersenne numbers and we introduce an extension of Fermat numbers, we find their generating functions binet formulas, related matrix representation and many other properties.
Shefa A. Bani Melhem, A. Al-Kateeb, Afnan Dagher   +2 more
semanticscholar   +1 more source