Results 31 to 40 of about 268 (182)
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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Three Diophantine equations concerning the polygonal numbers [PDF]
Notes on Number Theory and Discrete MathematicsMany authors investigated the problem about the linear combination of two polygonal numbers being a perfect square, i.e., the Diophantine equation mPₖ(x)+nPₖ(y)=z², where Pₖ(x) denotes the x-th k-polygonal number and m, n are positive integers.
Yong Zhang, Mei Jiang, Qiongzhi Tang
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Small solutions of linear Diophantine equations
Discrete Mathematics, 1986 Given a system of linear diophantine equations and let (*) \(Ax=B\) be its matrix form, where \(A=(a_{ij})\) is a \(m\times n\), \(x=(x_k)\) and \(B=(a_{k,n+1})\) are \(m\times 1\) matrices. Further, given integers \(1\leq j_1< \cdots < j_m\leq n+1\), let \(d_{j_1,\ldots, j_m} = \det (a_{i,j_r}),\) \(1\leq i,r\leq m\), \(X=\sup \{| d_{j_1,\ldots, j_m}|:
I. Borosh, M. Flahive, B. Treybig
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Geometry of the Minimal Solutions of a Linear Diophantine Equation [PDF]
SIAM Journal on Discrete Mathematics, 2021 12 pages; To appear in SIAM J.
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A Study of Symbolic 2-Plithogenic Split-Complex Linear Diophantine Equations in Two Variables [PDF]
Neutrosophic Sets and Systems, 2023 The equation 𝐴𝑋 + 𝐵𝑌 = 𝐶 is called symbolic 2-plithogenic linear Diophantine equation with two variables if 𝐴, 𝐵, 𝑋, 𝑌, 𝐶 are symbolic 2-plithogenic split-complex integers.
Rama Asad Nadweh +3 more
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On a few Diophantine equations, in particular, Fermat's last theorem
International Journal of Mathematics and Mathematical Sciences, 2003 This is a survey on Diophantine equations, with the purpose being to give the flavour of some known results on the subject and to describe a few open problems.
C. Levesque
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Elementary Deduction Problem for Locally Stable Theories with Normal Forms [PDF]
Electronic Proceedings in Theoretical Computer Science, 2013 We present an algorithm to decide the intruder deduction problem (IDP) for a class of locally stable theories enriched with normal forms. Our result relies on a new and efficient algorithm to solve a restricted case of higher-order associative ...
Mauricio Ayala-Rincón +2 more
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The Mathematical Safe Problem and Its Solution (Part 2)
Кібернетика та комп'ютерні технології, 2021 Introduction. The problem of mathematical safe arises in the theory of computer games and cryptographic applications. The article considers numerous variations of the mathematical safe problem and examples of its solution using systems of linear ...
Sergii Kryvyi, Hryhorii Hoherchak
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Diophantine Equations Related with Linear Binary Recurrences
Iranian Journal of Mathematical Sciences and Informatics, 2022 Summary: In this paper we find all solutions of four kinds of the Diophantine equations \[ x^2 \pm V_t xy-y^2 \pm x=0 \text{ and } x^2 \pm V_txy-y^2 \pm y=0, \] for an odd number \(t\), and, \[ x^2 \pm V_txy+y^2-x=0 \text{ and } x^2 \pm V_txy+y^2-y=0, \] for an even number \(t\), where \(V_n\) is a generalized Lucas number.
Kilic, Emrah, Akkus, Ilker, Omur, Nese
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Mulatu Numbers Which Are Concatenation of Two Fibonacci Numbers
Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 2023 Let (M_k) be the sequence of Mulatu numbers defined by M_0=4, M_1=1, M_k=M_(k-1)+M_(k-2) and (F_k) be the Fibonacci sequence given by the recurrence F_k=F_(k-1)+F_(k-2) with the initial conditions F_0=0, F_1=1 for k≥2.
Fatih Erduvan, Merve Güney Duman
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