Results 91 to 100 of about 11,736 (207)
Extension of a Diophantine triple with the property D(4)
, 2021 We give an upper bound on the number of extensions of a triple to a quadruple for the Diophantine m- tuples with the property D(4).
Bliznac Trebješanin, Marija
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The Number of Partitions of a Set and Superelliptic Diophantine Equations [PDF]
, 2020 In this chapter we start by presenting some key results concerning the number of ordered k-partitions of multisets with equal sums. For these we give generating functions, recurrences and numerical examples.
Dorin Andrica +5 more
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A Linear Diophantine Fuzzy Graph-Theoretic Approach for Planar Dynamic Traffic Optimization
Applied Computational Intelligence and Soft ComputingDynamic urban traffic signal control systems face uncertainties such as fluctuating vehicle densities, unpredictable incidents, and varying driver behaviors, making precise decision-making highly challenging.
Waheed Ahmad Khan +4 more
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On the Relationship Between Matiyasevich's and Smorynski's Theorems
Scientific Annals of Computer Science, 2019 Let R be a non-zero subring of Q with or without 1. We assume that for every positive integer n there exists a computable surjection from N onto Rn. Every R \in {Z,Q} satisfi es these conditions.
Agnieszka Peszek, Apoloniusz Tyszka
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A CLASS OF DIOPHANTINE EQUATIONS [PDF]
Proceedings of the National Academy of Sciences, 1959 Nach Verf. hat \[ \alpha^x+\beta^x=\alpha^n+\beta^n,\quad \alpha,\beta=\tfrac 12 (1\pm\sqrt{-7}), \] für gegebene \(n\) höchstens zwei Lösungen und für \(n=2^m\) genau die triviale Lösung \(x=2^m\).
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Integrality and the Laurent phenomenon for Somos 4 and Somos 5 sequences [PDF]
, 2008 Somos 4 sequences are a family of sequences defined by a fourth-order quadratic recurrence relation with constant coefficients. For particular choices of the coefficients and the four initial data, such recurrences can yield sequences of integers.
Swart, Christine, Hone, Andrew N.W.
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, 1967 Formulae are given furnishing all non-trivial integer solutions of the equation \[ (x^2-t^2)(y^2-t^2)=\biggl(\biggl({y-x\over 2}\biggr)^2-t^2\biggr)^2 \] considered for \(t=1\) by the reviewer and \textit{W. Sierpiński} [Elem. Math. 18, 132--133 (1963; Zbl 0126.07301)].
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A Diophantine equation appearing in Diophantine approximation
Indagationes Mathematicae, 2001 All Diophantine equations \(ax^2+ by^2+ cz^2= 1+dxyz\) with \(a,b,c,d\in \mathbb{N}\) and \(a\mid d\), \(b\mid d\), \(c\mid d\), with solutions \((x,y,z)\in \mathbb{N}^3\) are classified. Equations of this type occur in connection with the approximation spectrum for quaternions.
Jin, Yuan, Schmidt, Asmus L.
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On Diophantine singlefold specifications
Le MatematicheSummary: Consider an \((m+1)\)-ary relation \(\mathcal{R}\) over the set \(\mathbb{N}\) of natural numbers. Does there exist an arithmetical formula \(\varphi (a_0, \ldots, a_m, x_1, \ldots, x_k)\), not involving universal quantifiers, negation, or implication, such that representation and univocity conditions, viz., \[ \begin{aligned} \mathcal{R ...
Domenico Cantone +2 more
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Application of the group action approach to solving linear Diophantine equations [PDF]
Известия Саратовского университета. Новая серия: Математика. Механика. ИнформатикаThe article substantiates a method for solving linear Diophantine equations using the theory of group actions. The purpose of this paper is to introduce actions of certain groups on the set of linear Diophantine equations and to study their ...
Chistov, Ivan Sergeevich +1 more
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