Results 31 to 40 of about 9,626 (197)
Affine–Hill cipher from Hadamard-type Fibonacci–Mersenne and Fibonacci-balancing p-sequences [PDF]
Notes on Number Theory and Discrete MathematicsIn 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 +2 more
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Pseudo-random number generators for Monte Carlo simulations on Graphics Processing Units [PDF]
, 2010 Basic uniform pseudo-random number generators are implemented on ATI Graphics Processing Units (GPU). The performance results of the realized generators (multiplicative linear congruential (GGL), XOR-shift (XOR128), RANECU, RANMAR, RANLUX and Mersenne ...
Anderson +25 more
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1, 2, and 6 qubits, and the Ramanujan-Nagell theorem [PDF]
, 2012 A conjecture of Ramanujan that was later proved by Nagell is used to show on the basis of matching dimensions that only three $n$-qubit systems, for $n=1, 2, 6$, can share an isomorphism of their symmetry groups with the rotation group of corresponding ...
Pavlyukh, Yaroslav, Rau, A. R. P.
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The First Study of Mersenne--Leonardo Sequence
Communications in Advanced Mathematical SciencesIn 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 +1 more
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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
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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
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Probabilistic Methods on Erdos Problems [PDF]
, 2013 The study of perfect numbers dates back to Euler and Mersenne. A perfect number is a number that is equal to the sum of its proper divisors which are said to include the multiplicative unit 1.
Gilbert, Jesse
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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
Generalized Commutative Mersenne and Mersenne–Lucas Quaternion Polynomials
Annales Mathematicae SilesianaeGeneralized 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 +2 more
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Mersenne Numbers: consolidated results [PDF]
, 1986 This document provides and comments on the results of the Lucas-Lehmer testing and/or partial factorisation of all Mersenne Numbers Mp = 2^p-1 where p is prime and less than 100,000. Previous computations have either been confirmed or corrected.
Haworth, Guy McCrossan +4 more
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