Results 31 to 40 of about 4,123,026 (315)
On some Diophantine equations involving balancing numbers
, 2021 In this paper, we find all the solutions of the Diophantine equation B 1 + 2B p 2 + · · ·+ kB p k = B n in positive integer variables (k, n), where Bi is the ith balancing number if the exponents p, q are included in the set {1, 2}.
E. Tchammou, A. Togbé
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A study on the number of edges of some families of graphs and generalized Mersenne numbers
Ratio Mathematica, 2022 The relationship between the Nandu sequence of the SM family of graphs and the Generalized Mersenne numbers is demonstrated in this study. Nandu sequences are related to the two families of SM sum graphs and SM Balancing graphs.
K.G. Sreekumar +3 more
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Journal of Innovative Applied Mathematics and Computational Sciences, 2021 In this paper, closed forms of the sum formulas $\sum_{k=0}^{n}x^{k}W_{mk+j}^{2}$ for generalized balancing numbers are presented. As special cases, we give sum formulas of balancing, modified Lucas-balancing and Lucas-balancing numbers.
Yüksel Soykan +2 more
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An exponential Diophantine equation related to the difference between powers of two consecutive Balancing numbers [PDF]
, 2018 In this paper, we find all solutions of the exponential Diophantine equation $B_{n+1}^x-B_n^x=B_m$ in positive integer variables $(m, n, x)$, where $B_k$ is the $k$-th term of the Balancing sequence.Comment: Comments are ...
Faye, Bernadette +3 more
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On the Partial Finite Alternating Sums of Reciprocals of Balancing and Lucas-Balancing Numbers
Discussiones Mathematicae - General Algebra and Applications, 2020 In this note, the finite alternating sums of reciprocals of balancing and Lucas-balancing numbers are considered and several identities involving these sums are deduced.
Dutta Utkal Keshari, Ray Prasanta Kumar
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The Tribonacci-type balancing numbers and their applications [PDF]
Mathematica Moravica, 2023 N this paper, we define the Tribonacci-type balancing numbers via a Diophantine equation with a complex variable and then give their miscellaneous properties. Also, we study the Tribonacci-type balancing sequence modulo m and then obtain some interesting
Hulku Sakıne, Devec Ömür
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Solutions of the Diophantine Equations Br=Js+Jt and Cr=Js+Jt
Journal of Mathematics, 2023 Let Brr≥0, Jrr≥0, and Crr≥0 be the balancing, Jacobsthal, and Lucas balancing numbers, respectively. In this paper, the diophantine equations Br=Js+Jt and Cr=Js+Jt are completely solved.
Ahmed Gaber, Mohiedeen Ahmed
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Balancing and Lucas-balancing Numbers With Real Indices [PDF]
, 2015 In this thesis, we have studied the balancing and Lucas-balancing numbers for real indices. Also we have discussed some properties of balancing numbers with real numbers.
Tanty, Sephali
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Repdigits as sums of three balancing numbers
Mathematica Slovaca, 2020 Let {Bn}n≥0 be the sequence of Balancing numbers defined by B0 = 0, B1 = 1, and Bn+2 = 6Bn+1 − Bn for all n ≥ 0. In this paper, we find all repdigits in base 10 which can be written as a sum of three Balancing numbers.
M. Ddamulira
semanticscholar +1 more source
Simulation Verification of Balancing System Based on Number of Cells
Communications, 2021 This paper deals with the simulation verification of balancing systems with different numbers of batteries. There is a simulation model of the battery with adjustable inputs and a simulation model of flyback converter. These components are interconnected
Marek Šimčák, Matúš Danko
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