Results 41 to 50 of about 237,797 (205)
Balancing and Lucas-Balancing Numbers and their Application to Cryptography [PDF]
, 2016 It is well known that, a recursive relation for the sequence  is an equation that relates  to certain of its preceding terms .
Kumar Ray, Prasanta +2 more
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Practical numbers in Lucas sequences [PDF]
Quaestiones Mathematicae, 2018 A practical number is a positive integer n such that all the positive integers m ≤ n can be written as a sum of distinct divisors of n. Let (un)n≥0 be the Lucas sequence satisfying u0 = 0, u1 = 1, and un+2 = aun+1 + bun for all integers n ≥ 0, where a and b are fixed nonzero integers. Assume a(b + 1) even and a 2 + 4b > 0.
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On the Diophantine equation x^2+7^{alpha}.11^{beta}=y^n [PDF]
, 2012 In this paper, we give all the solutions of the Diophantine equation x^2+7^{alpha}.11^{beta}=y^n, in nonnegative integers x, y, n>=3 with x and y coprime, except for the case when alpha.x is odd and beta is even.Comment: to appear in Miskolc Mathematical
Soydan, Gokhan
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Mersenne-Horadam identities using generating functions
Karpatsʹkì Matematičnì Publìkacìï, 2020 The main object of the present paper is to reveal connections between Mersenne numbers $M_n=2^n-1$ and generalized Fibonacci (i.e., Horadam) numbers $w_n$ defined by a second order linear recurrence $w_n=pw_{n-1}+qw_{n-2}$, $n\geq 2$, with $w_0=a$ and ...
R. Frontczak, T.P. Goy
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On the common modulus attack into the LUC4,6 cryptosystem [PDF]
, 2014 The LUC4,6 cryptosystem is a system analogy with RSA cryptosystem and extended from LUC and LUC3 cryptosystems. The process of encryption and decryption are derived from the fourth order linear recurrence sequence and based on Lucas function.
Koo, Lee Feng +3 more
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Some properties of the generalized (p,q)- Fibonacci-Like number
MATEC Web of Conferences, 2018 For the real world problems, we use some knowledge for explain or solving them. For example, some mathematicians study the basic concept of the generalized Fibonacci sequence and Lucas sequence which are the (p,q) – Fibonacci sequence and the (p,q ...
Suvarnamani Alongkot
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On Bicomplex Jacobsthal-Lucas Numbers
Journal of Mathematical Sciences and Modelling, 2020 In this study we introduced a sequence of bicomplex numbers whose coefficients are chosen from the sequence of Jacobsthal-Lucas numbers. We also present some identities about the known some fundamental identities such as the Cassini's, Catalan's and ...
Serpil Halıcı
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On $k$-Fibonacci balancing and $k$-Fibonacci Lucas-balancing numbers
Karpatsʹkì Matematičnì Publìkacìï, 2021 The balancing number $n$ and the balancer $r$ are solution of the Diophantine equation $$1+2+\cdots+(n-1) = (n+1)+(n+2)+\cdots+(n+r). $$ It is well known that if $n$ is balancing number, then $8n^2 + 1$ is a perfect square and its positive square root is
S.E. Rihane
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Some Polynomial Sequence Relations
Mathematics, 2019 We give some polynomial sequence relations that are generalizations of the Sury-type identities. We provide two proofs, one based on an elementary identity and the other using the method of generating functions.
Chan-Liang Chung
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On the discriminator of Lucas sequences. II
, 2023 25 pages, 7 ...
Ferrari, ., Luca, F., Moree, P.
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