Results 21 to 30 of about 10,192,155 (339)
Average Case Error Estimates of the Strong Lucas Test [PDF]
arXiv.org, 2023 Reliable probabilistic primality tests are fundamental in public-key cryptography. In adversarial scenarios, a composite with a high probability of passing a specific primality test could be chosen.
Semira Einsele, Kenneth G. Paterson
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On the k-Fibonacci and k-Lucas spinors
Notes on Number Theory and Discrete Mathematics, 2023 In this paper, we introduce a new family of sequences called the k-Fibonacci and k-Lucas spinors. Starting with the Binet formulas we present their basic properties, such as Cassini’s identity, Catalan’s identity, d’Ocagne’s identity, Vajda’s identity ...
Munesh Kumari, K. Prasad, R. Frontczak
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The p-Frobenius and p-Sylvester numbers for Fibonacci and Lucas triplets. [PDF]
Mathematical biosciences and engineering : MBE, 2022 In this paper we study a certain kind of generalized linear Diophantine problem of Frobenius. Let $ a_1, a_2, \dots, a_l $ be positive integers such that their greatest common divisor is one.
T. Komatsu, Ha Ying
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Exact divisibility by powers of the integers in the Lucas sequence of the first kind
AIMS Mathematics, 2020 Lucas sequence of the first kind is an integer sequence $(U_n)_{n\geq0}$ which depends on parameters $a,b\in\mathbb{Z}$ and is defined by the recurrence relation $U_0=0$, $U_1=1$, and $U_n=aU_{n-1}+bU_{n-2}$ for $n\geq2$. In this article, we obtain exact
Kritkhajohn Onphaeng +1 more
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Remote Sensing, 2022 One of the most challenging aspects of obtaining detailed and accurate land-use and land-cover (LULC) maps is the availability of representative field data for training and validation.
Babak Ghassemi +5 more
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Some new properties of hyperbolic k-Fibonacci and k-Lucas octonions [PDF]
Notes on Number Theory and Discrete MathematicsThe aim of this paper is to establish some novel identities for hyperbolic k-Fibonacci octonions and k-Lucas octonions. We prove these properties using the identities of k-Fibonacci and k-Lucas numbers, which we determined previously.
A. D. Godase
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Hybrid hyper-Fibonacci and hyper-Lucas numbers
Notes on Number Theory and Discrete Mathematics, 2023 Different number systems have been studied lately. Recently, many researchers have considered the hybrid numbers which are generalization of the complex, hyperbolic and dual number systems.
Yasemin Alp
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On divisors of Lucas and Lehmer numbers [PDF]
Acta Mathematica, 2013 Let u(n) be the n-th term of a Lucas sequence or a Lehmer sequence.In this article we shall establish an estimate from below for the greatest prime factor of u(n) which is of the form nexp(logn/104loglogn). In so doing we are able to resolve a question of Schinzel from 1962 and a conjecture of Erdos from 1965.In addition we are able to give the first ...
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Sums of Pell/Lucas Polynomials and Fibonacci/Lucas Numbers
Mathematics, 2022 Seven infinite series involving two free variables and central binomial coefficients (in denominators) are explicitly evaluated in closed form. Several identities regarding Pell/Lucas polynomials and Fibonacci/Lucas numbers are presented as consequences.
Dongwei Guo, Wenchang Chu
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Bi-Periodic (p,q)-Fibonacci and Bi-Periodic (p,q)-Lucas Sequences
Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 2023 In this paper, we define bi-periodic (p,q)-Fibonacci and bi-periodic (p,q)-Lucas sequences, which generalize Fibonacci type, Lucas type, bi-periodic Fibonacci type and bi-periodic Lucas type sequences, using recurrence relations of (p,q)-Fibonacci and (p,
Yasemin Taşyurdu +1 more
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