Results 101 to 110 of about 1,108 (208)
On Mersenne’s number 𝑀₂₂₇ and cognate data [PDF]
Bulletin of the American Mathematical Society, 1948 condition XX-i /^^O. But ^2—^1 shows that this condition is not sufficient. Polya remarked that if (25) has infinitely many solutions we can not have a i^O, #1+02 se 0, • • • , # i+#2+ • • • +an^0t The characterization of the forms which satisfy (26) seems a difficult problem. Finally we mention two more questions: (1) Cantheinequal i t ies^ n +i-^n pk-
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Mersenne Numbers: consolidated results
, 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.
Hunt, David +4 more
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On Squaring Modulo Mersenne Numbers [PDF]
, 2022 During the design of a new primitive inspired by Squash we accidentally stumbled on the observation described in this note. Let $n$ be a $k$-bit Mersenne number whose factors are unknown. Consider an $\ell$-bit secret number $x=2^{k/2}a+b$.
Ofer Yifrach-Stav, David Naccache
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Improved Spectrum Coexistence in 2.4 GHz ISM Band Using Optimized Chaotic Frequency Hopping for Wi-Fi and Bluetooth Signals. [PDF]
Sensors (Basel), 2023 Eltholth AA.
europepmc +1 more source
Gaussian Mersenne numbers and generalized Mersenne quaternions [PDF]
Notes on Number Theory and Discrete Mathematics, 2019 Ahmet Daşdemir, Göksal Bilgici
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On the emergence of the Quanta Prime sequence
Arab Journal of Basic and Applied SciencesThis paper presents the Quanta Prime Sequence (QPS) and its foundational theorem, showcasing a unique class of polynomials with substantial implications.
Moustafa Ibrahim
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Primality-testing Mersenne Numbers (II)
, 1986 Reports the factor-filtering and primality-testing of Mersenne Numbers Mp for p < 100000, the latter using the ICL 'DAP' Distributed Array ...
Haworth, Guy McCrossan
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, 1999 . There is a well known shortcut for modular multiplication modulo a Mersenne number, performing modular reduction without integer division. We generalize this technique to a larger class of primes, and discuss parameter choices which are particularly ...
Jerome A. Solinas
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MERSENNE AND HADAMARD MATRICES CALCULATION BY SCARPIS METHOD [PDF]
Научно-технический вестник информационных технологий, механики и оптики, 2014 Purpose. The paper deals with the problem of basic generalizations of Hadamard matrices associated with maximum determinant matrices or not optimal by determinant matrices with orthogonal columns (weighing matrices, Mersenne and Euler matrices, ets ...
N. A. Balonin +2 more
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A Study On Generalized Mersenne Numbers
, 2021 In this paper, we introduce the generalized Mersenne sequence and we deal with, in detail, two special cases, namely, Mersenne and Mersenne-Lucas sequences.
Soykan, Yüksel
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