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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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Journal of Physics: Conference Series, 2019 This research may provide the solutions (if any) from the Non-linear Diophantine equation (7k — 1)x + (7k )y = Z2.There are 3 possibilities to determine the solutions from the Non-linear Diophantine equation: single solution, multiple solutions, and no ...
R. Rahmawati +3 more
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Spectrum sensing based on high/low sensing times
e-Prime: Advances in Electrical Engineering, Electronics and Energy, 2023 Cognitive Radio spectrum sensing is one of the important technique to utilize the unused specturm for secondary user signal transmission without interference with the primary users of the spectrum.
Ramamurthy Garimella +1 more
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Solutions to Non-Linear Diophantine Equation Pχ+ (P+5)y =z2 with P is Mersenne Prime
International journal of recent technology and engineering, 2019 This research seeks for a solution (if any) to non-linear Diophantine equation 2 ( 5) x y p p z with p is Mersenne prime. There are 3 possibilities of solution to the non-linear Diophantine equation, which are single solution, many solutions, or no
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An inhomogeneous wave equation and non-linear Diophantine approximation [PDF]
, 2008 A non-linear Diophantine condition involving perfect squares and arising from an inhomogeneous wave equation on the torus guarantees the existence of a smooth solution.
Kristensen, S. +3 more
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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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European Journal of Educational Research, 2022 Prospective teachers facing the 21st century are expected to have the ability to solve problems with a computer mindset. Problems in learning mathematics also require the concept of computational thinking (CT).
Neneng Aminah +3 more
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Using Matrices to Balance Chemical Reactions and Modeling the Implications of a Balanced Reaction
Undergraduate Journal of Mathematical Modeling: One + Two, 2019 This paper explores an alternative way to balancing equations of chemical reactions and understanding why it is necessary to use balanced equations in science.
Emilee Barrett
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Algorithms for the Solution of Systems of Linear Diophantine Equations [PDF]
SIAM Journal on Computing, 1982 Two algorithms for the solution of linear Diophantine systems, which well restrain intermediate expression swell, are presented. One is an extension and improvement of Kannan and Bachem’s algorithm for the Smith and the Hermite normal forms of a nonsingular square integral matrix.
Tsu-Wu J. Chou, George E. Collins
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On the statistics of the minimal solution of a linear Diophantine equation and uniform distribution of the real part of orbits in hyperbolic spaces [PDF]
, 2007 We study a variant of a problem considered by Dinaburg and Sinai on the statistics of the minimal solution to a linear Diophantine equation. We show that the signed ratio between the Euclidean norms of the minimal solution and the coefficient vector is ...
Morten S. Risager, Z. Rudnick
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