Results 21 to 30 of about 180 (147)
Sequences in finite fields yielding divisors of Mersenne, Fermat and Lehmer numbers, II [PDF]
Notes on Number Theory and Discrete MathematicsLet ρ be an odd prime ≥ 11. In Part I, starting from an M-cycle in a finite field 𝔽_ρ, we have established how the divisors of Mersenne, Fermat and Lehmer numbers arise.
A. M. S. Ramasamy
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Splitting Sequences for Coding and Hybrid Incremental ARQ with Fragment Retransmission
Mathematics, 2021 This paper proposes a code defined on a finite ring ℤpM, where pM = 2m−1 is a Mersenne prime, and m is a binary size of ring elements. The code is based on a splitting sequence (splitting set) S, defined for the given multiplier set E=±20, ±21,…, ±2m−1 ...
Dragana Bajić +2 more
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Sequences in finite fields yielding divisors of Mersenne, Fermat and Lehmer numbers, I [PDF]
Notes on Number Theory and Discrete MathematicsThe aim of this work is to present a method using the cyclic sequences {Mₖ},{θₜₖ} and {ψₜₖ} in the finite fields 𝔽_ρ, with ρ a prime, that yield divisors of Mersenne, Fermat and Lehmer numbers.
A. M. S. Ramasamy
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Computer Experiments with Mersenne Primes [PDF]
Computational Methods in Science and Technology, 2013 We have calculated on the computer the sum $\bar{\BB}_M$ of reciprocals of all 47 known Mersenne primes with the accuracy of over 12000000 decimal digits. Next we developed $\bar{\BB}_M$ into the continued fraction and calculated geometrical means of the partial denominators of the continued fraction expansion of $\bar{\BB}_M$. We get values converging
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Acerca de algunos exponentes de Mersenne (About some Mersenne exponents)
Revista Digital Matemática, Educación e InternetLos números primos de Mersenne crecen de manera vertiginosa y se vuelven intratables con las herramientas de cómputo actuales. En este trabajo se repasan brevemente las cadenas de Mersenne para mostrar cómo ese crecimiento exponencial impone un límite en
Gerardo Miramontes de León
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Arab Journal of Basic and Applied SciencesThis paper introduces a new key geometric way to understand Mersenne prime numbers. It discovers a shape called the Mersenne Star, which appears naturally from a special sequence named the Quanta Prime Sequence (QPS).
Moustafa Ibrahim
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Some new results on the largest cycle consisting of quadratic residues [PDF]
Notes on Number Theory and Discrete MathematicsThe length of the largest cycle consisting of quadratic residues of a positive integer n is denoted by L(n). In this paper, we have obtained a formula for finding L(p), where p is a prime. Also, we attempt to characterize a prime number p in terms of the
Prabin Das, Pinkimani Goswami
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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
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Complexity Lower Bound for Boolean Functions in the Class of Extended Operator Forms
Известия Иркутского государственного университета: Серия "Математика", 2019 Starting with the fundamental work of D.E.Muller in 1954, the polynomial representations of Boolean functions are widely investigated in connection with the theory of coding and for the synthesis of circuits of digital devices.
A.S. Baliuk
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FPGA Realization of a Novel Hyperchaos Augmented Image Encryption Algorithm
IET Computers &Digital Techniques, Volume 2026, Issue 1, 2026.With the rapid growth of multimedia communication, protecting image data has become increasingly critical. This article proposes a novel 3‐stage hyperchaos‐based augmented image encryption technique (3SHAIET) that utilizes a three‐stage process with chaotic systems of increasing dimensionality (e.g., six‐dimensional [6D], 8D, and 9D) to enhance ...
Wassim Alexan +6 more
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