Results 81 to 90 of about 839 (184)
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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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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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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, 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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Introduction to Diophantine Approximation
Formalized Mathematics, 2015 Abstract In this article we formalize some results of Diophantine approximation, i.e. the approximation of an irrational number by rationals. A typical example is finding an integer solution (x, y) of the inequality |xθ − y| ≤ 1/x, where 0 is a real number. First, we formalize some lemmas about continued fractions. Then we prove that the
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On the Existence of Solutions of Diophantine Equations Related to Subbalancing Numbers
Journal of MathematicsIn this paper, we introduce a new sequence of subbalancing numbers by considering balancing numbers as the values of D in the Diophantine equations provided by subbalancing numbers.
Selin Sarı, Gül Karadeniz-Gözeri
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From Diophantine approximations to Diophantine equations
Keldysh Institute Preprints, 2016 Summary: Let in the real \(n\)-dimensional space \(\mathbb{R}^n=\{X\}\) be given \(m\) real homogeneous forms \(f_i(X), i=1,\dotsc,m, 2\leqslant m\leqslant n\). The convex hull of the set of points \(G(X)=(|f_1(X)|,\dotsc,|f_m(X)|)\) for integer \(X\in\mathbb Z^n\) in many cases is a convex polyhedral set. Its boundary for \(||X||
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AxiomsThe theory of spherical linear Diophantine fuzzy sets (SLDFS) boasts several advantages over existing fuzzy set (FS) theories such as Picture fuzzy sets (PFS), spherical fuzzy sets (SFS), and T-spherical fuzzy sets (T-SFS).
Mani Parimala, Saeid Jafari
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Transactions on Fuzzy Sets and SystemsAlzheimers disease is an unpredictable and progressive neurodegenerative disorder that initially affects memory thinking and behavior. Some key features of Alzheimers disease are memory loss, cognitive decline, behavioral changes, disorientation ...
Zeeshan Ali
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四川大学学报. 自然科学版, 1962 Recently, Chao Koc 1 3' E2:i proved that the diophantine equationshave no integral solutions x,y with xy dpO..n this paper, I shall prove that the diophantine equation is impossible when p = 5, 7, 11, 13, 17, 19, 23, 29, 41, 43, 47,.> -r. 53, 61, 71, 79,
张世勋
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