Results 41 to 50 of about 1,108 (208)

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

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

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

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

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

Application of Statistical Shape Models to Standard Lumbar MRI for Stenosis Treatment Stratification: Severe Versus Normal Stenosis

JOR SPINE, Volume 9, Issue 2, June 2026.
Statistical shape models (SSMs) derived from standard 2D lumbar MRIs capture coordinated morphological features that distinguish severe from normal spinal stenosis. Both intervertebral disc and combined models provide strong discriminatory power, comparable to or exceeding traditional anatomical measurements.
Mary H. Foltz, Alexandra Seidenstein, Wesley M. Durand, Amit Jain, Jill M. Middendorf   +4 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

Converting Binary Floating‐Point Numbers to Shortest Decimal Strings: An Experimental Review

Software: Practice and Experience, Volume 56, Issue 4, Page 462-478, April 2026.
ABSTRACT Background When sharing or logging numerical data, we must convert binary floating‐point numbers into their decimal string representations. For example, the number π might become 3.1415927. Engineers have perfected many algorithms for producing such accurate, short strings.
Jaël Champagne Gareau, Daniel Lemire
wiley   +1 more source

On the intersections of nilpotent subgroups in simple groups

Proceedings of the London Mathematical Society, Volume 132, Issue 3, March 2026.
Abstract Let G$G$ be a finite group and let Hp$H_p$ be a Sylow p$p$‐subgroup of G$G$. A recent conjecture of Lisi and Sabatini asserts the existence of an element x∈G$x \in G$ such that Hp∩Hpx$H_p \cap H_p^x$ is inclusion‐minimal in the set {Hp∩Hpg:g∈G}$\lbrace H_p \cap H_p^g \,:\, g \in G\rbrace$ for every prime p$p$.
Timothy C. Burness, Hong Yi Huang
wiley   +1 more source