Results 91 to 100 of about 1,246,845 (203)
Arab Journal of Basic and Applied SciencesMersenne primes, renowned for their captivating form as [Formula: see text] have intrigued mathematicians for centuries. In this paper, we embark on a captivating quest to unveil the intricate nature of Mersenne primes, seamlessly integrating methods ...
Moustafa Ibrahim
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Applied Computational Intelligence and Soft Computing, Volume 2026, Issue 1, 2026.Images transmitted across open networks, such as the Internet, are inherently vulnerable to eavesdropping, unauthorized access, and data tampering. Sensitive image categories, including medical, military, biometric, and legal images, often require a higher level of protection than public protocols provide. Moreover, the large size, high redundancy, and
Rami Sihwail +3 more
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Neural Ordinary Differential Equation With Grünwald–Letnikov Fractional Momentum
Complexity, Volume 2026, Issue 1, 2026.Forecasting short annual time series is challenging because limited observations increase the risks of unstable optimization, overfitting, and information leakage. This study proposes a standard first‐order neural ordinary differential equation trained with finite‐memory Grünwald–Letnikov fractional momentum.
Wei Yang, Shikha Binwal
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On generalized Mersenne numbers, their interpretations and matrix generators [PDF]
, 2018 In this paper we introduce generalized Mersenne numbers. We shall present some of their interpretations and matrix generators which are very useful for determining ...
Włoch, Andrzej, Ochalik, Paweł
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A Study on the k-Mersenne and k-Mersenne-Lucas Sequences
Universal Journal of Mathematics and ApplicationsIn this study, we examine an application of $k-$Mersenne and $k-$Mersenne-Lucas sequences. We present the Catalan transforms of these sequences and give the properties of these Catalan transforms. Catalan transforms of $k-$Mersenne and $k-$Mersenne-Lucas
Mine Uysal +3 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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A Generalization of Gaussian Balancing and Gaussian Balancing‐Lucas Numbers With Applications
International Journal of Mathematics and Mathematical Sciences, Volume 2026, Issue 1, 2026.In this paper, we study a generalization of Gaussian balancing and Gaussian Lucas‐balancing numbers, we find their generating functions, Binet formulas, related matrix representation, and many other properties. Also, we provide some applications in cryptography.
T. Al-Asoully +2 more
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On Generalized p-Mersenne Numbers
, 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.
Yüksel Soykan
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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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On Mersenne’s number 𝑀₁₉₉ and Lucas’s sequences [PDF]
Bulletin of the American Mathematical Society, 1947 On July 27, 1946 the writer finished calculating the 198th remainder of the Lucasian sequence 3, 7, 47, • • • as applied to the 60-digit Mersenne number 2 1 9 9 -1=80346 90221 29495 13777 09810 46170 ...
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