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On Pell, Pell-Lucas, and balancing numbers
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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A note on the integer solutions ofhyperelliptic equations [PDF]
Colloquium Mathematicum, 1995 The following interesting theorem is proved: Let \(f(x)= x^ m+ a_ 1 x^{m-1}+ \cdots+ a_ m\in \mathbb{Z} [x]\) with \(m\geq 2\) and not all \(a_ i\)'s equal to zero and the first non-zero coefficient coprime to some integer \(n\geq 2\). If \(mn\geq 6\) and \(m\equiv 0\pmod n\) then all integer solutions \((x,y)\) of \(y^ n= f(x)\) satisfy \(| x|< (4m H)^
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Abstract and Applied Analysis, 2012 We present some conditions for the existence and uniqueness of almost periodic solutions of 𝑁th-order neutral differential equations with piecewise constant arguments of the form (𝑥(𝑡)+𝑝𝑥(𝑡−1))(𝑁)=𝑞𝑥([𝑡])+𝑓(𝑡), here [⋅] is the greatest integer function ...
Rong-Kun Zhuang
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Alternative solutions to the Legendre's equation x²+ky²=z² [PDF]
Notes on Number Theory and Discrete MathematicsIn this paper, we aim to provide alternative solutions of the Legendre's equation x²+ky²=z², where k is a square-free positive integer. The results also lead to solutions of the well-known Pythagorean triples and Eisenstein triples.
Kanwara Mukkhata, Sompong Chuysurichay
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Integer solutions to x2+ y2= z2−k for a fixed integer value k
Involve, a Journal of Mathematics, 2017 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Boyer, Wanda +4 more
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The fractional analysis of thermo-elasticity coupled systems with non-linear and singular nature
Scientific ReportsIt is mentioned that understanding linear and non-linear thermo-elasticity systems is important for understanding temperature, elasticity, stresses, and thermal conductivity.
Abdur Rab +6 more
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Real And Gaussian Integer Solutions To
, 2018 The quadratic equation with four unknowns given by is analysed for its non-zero distinct integer solutions and Gaussian integer solutions. Different choices of solutions in real and Gaussian integers are obtained. A general formula for obtaining sequence of solutions (real and complex) based on its given solution is illustrated.
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Integer Number Solutions Of Linear Systems
, 2007 Let’s consider a linear system with all coefficients being integer numbers (the case with rational coefficients is reduced to the same).
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Periodic solutions of arbitrary length in a simple integer iteration
Advances in Difference Equations, 2006 We prove that all solutions to the nonlinear second-order difference equation in integers yn+1 = ⌈ayn⌉-yn-1, {a ∈ ℝ:|a|<2, a≠0,±1}, y0, y1 ∈ ℤ, are periodic. The first-order system representation of this
Clark Dean
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Solution of integer quadratic programs
, 2009 Let $(QP)$ be an integer quadratic program that consists in minimizing a quadratic function subject to linear constraints. A such problem belongs to the class of $\mathcal{NP}\textrm{-Hard}$ problems. Standard solvers that use a Branch and Bound algorithm can efficiently solve $(QP)$ in the specific case where its objective function is convex. Thus, to
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