Results 21 to 30 of about 10,886,718 (351)
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 Mixed 𝐵-Concatenations of Pell and Pell–Lucas Numbers which are Pell Numbers [PDF]
Mathematica Pannonica, 2023 Let (𝑃𝑛)𝑛≥0 and (𝑄𝑛)𝑛≥0 be the Pell and Pell–Lucas sequences. Let 𝑏 be a positive integer such that 𝑏 ≥ 2. In this paper, we prove that the following two Diophantine equations 𝑃𝑛 = 𝑏𝑑𝑃𝑚 + 𝑄𝑘 and 𝑃𝑛 = 𝑏𝑑𝑄𝑚 + 𝑃𝑘 with 𝑑, the number of digits of 𝑃𝑘 or 𝑄𝑘 in ...
Kouessi Norbert Ad'edji +1 more
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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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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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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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Incomplete Tribonacci–Lucas Numbers and Polynomials [PDF]
Advances in Applied Clifford Algebras, 2014 In this paper, we define Tribonacci-Lucas polynomials and present Tribonacci-Lucas numbers and polynomials as a binomial sum. Then, we introduce incomplete Tribonacci-Lucas numbers and polynomials. In addition we derive recurrence relations, some properties and generating functions of these numbers and polynomials. Also, we find the generating function
Yilmaz, Nazmiye, Taskara, Necati
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, 2000 In this short paper I show how it is related to other famous unsolved problems in prime number theory. In order to do this, I formulate the main hypothetical result of this paper - a useful upper bound conjecture (Conjecture 3.), describing one aspect of
Saidak, F.
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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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On square Tribonacci Lucas numbers
Hacettepe Journal of Mathematics and Statistics, 2021 The Tribonacci-Lucas sequence {Sn}{Sn} is defined by the recurrence relation Sn+3=Sn+2+Sn+1+SnSn+3=Sn+2+Sn+1+Sn with S0=3, S1=1, S2=3.S0=3, S1=1, S2=3. In this note, we show that 11 is the only perfect square in Tribonacci-Lucas sequence for n≢1(mod32)n≢1(mod32) and n≢17(mod96).n≢17(mod96).
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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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