Results 11 to 20 of about 84,298 (262)
GAUSSIAN BALANCING NUMBERS AND GAUSSIAN LUCAS-BALANCING NUMBERS
Computer Engineering and Applications Journal, 2018 In this study we define Gaussian balancing numbers and Gaussian Lucas-balancing numbers. Then we obtain Binet-like formulas, generating functions and some identities related with Gaussian balancing numbers and Gaussian Lucas-balancing numbers. Moreover, we give the new properties of Gaussian balancing numbers and Gaussian Lucas-balancing numbers in ...
Prasanta Kumar Ray +2 more
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On Pell, Pell-Lucas, and balancing numbers [PDF]
Journal of Inequalities and Applications, 2018 In this paper, we derive some identities on Pell, Pell-Lucas, and balancing numbers and the relationships between them. We also deduce some formulas on the sums, divisibility properties, perfect squares, Pythagorean triples involving these numbers ...
Gül Karadeniz Gözeri
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On the properties of k-balancing numbers
Ain Shams Engineering Journal, 2018 In this study, a generalization of the sequence of balancing numbers called as k-balancing numbers is considered and some of their properties are established.
Prasanta Kumar Ray
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Solution to a pair of linear, two-variable, Diophantine equations with coprime coefficients from balancing and Lucas-balancing numbers [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 Let Bₙ and Cₙ be the n-th balancing and Lucas-balancing numbers, respectively. We consider the Diophantine equations ax + by = (1/2)(a - 1)(b - 1) and 1 + ax + by = (1/2)(a - 1)(b - 1) for (a,b) ∈ {(Bₙ,Bₙ₊₁), (B₂ₙ₋₁,B₂ₙ₊₁), (Bₙ,Cₙ), (Cₙ,Cₙ₊₁)} and ...
R. K. Davala
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Almost balancers, almost cobalancers, almost Lucas-balancers and almost Lucas-cobalancers [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 In this work, the general terms of almost balancers, almost cobalancers, almost Lucas-balancers and almost Lucas-cobalancers of first and second type are determined in terms of balancing and Lucas-balancing numbers.
Ahmet Tekcan, Esra Zeynep Türkmen
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The Balancing Number and Generalized Balancing Number of Some Graph Classes
The Electronic Journal of Combinatorics, 2023 Given a graph $G$, a 2-coloring of the edges of $K_n$ is said to contain a balanced copy of $G$ if we can find a copy of $G$ such that half of its edges is in each color class. If there exists an integer $k$ such that, for $n$ sufficiently large, every 2-coloring of $K_n$ with more than $k$ edges in each color contains a balanced copy of $G$, then we ...
Antoine Dailly +3 more
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Classes of gap balancing numbers [PDF]
Rocky Mountain Journal of Mathematics, 2021 14 ...
Bartz, Jeremiah +2 more
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On the Number of Balanced Lines [PDF]
Discrete & Computational Geometry, 2001 Given a set of \(n\) black and \(n\) white points in general position in the plane, a line \(l\) determined by two of them is said to be balanced, if each open halfplane determined by \(l\) contains exactly the same number of white points and black points. The authors prove that the number of balanced lines is at least \(n\).
János Pach, Rom Pinchasi
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Balances in the Set of Arithmetic Progressions
Axioms, 2021 This article focuses on searching and classifying balancing numbers in a set of arithmetic progressions. The sufficient and necessary conditions for the existence of balancing numbers are presented.
Chan-Liang Chung +2 more
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Repdigits in the base $b$ as sums of four balancing numbers [PDF]
Mathematica Bohemica, 2021 The sequence of balancing numbers $(B_n)$ is defined by the recurrence relation $B_n=6B_{n-1}-B_{n-2}$ for $n\geq2$ with initial conditions $B_0=0$ and $B_1=1.$ $B_n$ is called the $n$th balancing number. In this paper, we find all repdigits in the base $
Refik Keskin, Fatih Erduvan
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