Results 81 to 90 of about 20,123 (196)

Two exponential Diophantine equations [PDF]

Glasgow Mathematical Journal, 1997
In [3], two open problems were whether either of the diophantine equationswith n ∈ Z and f a prime number, is solvable if ω > 3 and 3 √ ω, but in this paper we allow f to be any (rational) integer and also 3 | ω. Equations of this form and more general ones can effectively be solved [5] with an advanced method based on analytical results, but the ...
openaire   +1 more source

On a class of diophantine equations

International Journal of Mathematics and Mathematical Sciences, 2002
Cohn (1971) has shown that the only solution in positive integers of the equation Y(Y+1)(Y+2)(Y+3)=2X(X+1)(X+2)(X+3) is X=4, Y=5. Using this result, Jeyaratnam (1975) has shown that the equation Y(Y+m)(Y+2m)(Y+3m)=2X(X+m)(X+2m)(X+3m) has only four pairs
Safwan Akbik
doaj   +1 more source

Is there a computable upper bound for the height of a solution of a Diophantine equation with a unique solution in positive integers?

Open Computer Science, 2017
Let Bn = {xi · xj = xk : i, j, k ∈ {1, . . . , n}} ∪ {xi + 1 = xk : i, k ∈ {1, . . . , n}} denote the system of equations in the variables x1, . . . , xn. For a positive integer n, let _(n) denote the smallest positive integer b such that for each system
Tyszka Apoloniusz
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On Diophantine equations involving Lucas sequences

Open Mathematics, 2019
In this paper, we shall study the Diophantine equation un = R(m)P(m)Q(m), where un is a Lucas sequence and R, P and Q are polynomials (under weak assumptions).
Trojovský Pavel
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G 2-manifolds from Diophantine equations

Journal of High Energy Physics
We argue that perturbatively flat vacua (PFVs) introduced in Phys. Rev. Lett. 124 (2020) 211603 are dual to M-theory compactifications on G 2-manifolds, enabling the enumeration of potentially novel G 2-manifolds via solutions to Diophantine equations in
Jakob Moritz
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О существовании порождающей КС-грамматики для произвольной линейной диофантовой системы [PDF]

Проблемы анализа, 1999
В работе доказывается существование контекстно-свободной грамматики и терминальной цепочки, порождающих произвольно заданную систему линейных диофантовых уравнений (ЛДУ).In this paper we prove the existance of a context-free grammar and a terminal string,
Корзун Д. Ж.
doaj  

Characterization of Diophantine Equations a+y2=z2, Pythagorean n-Tuples, and Algebraic Structures

International Journal of Mathematics and Mathematical Sciences
Let N,Z, and Q be the sets of natural, integers, and rational numbers, respectively. Our objective, involving a predetermined positive integer a, is to study a characterization of Diophantine equations of the form a+y2=z2. Building on this result, we aim
Roberto Amato
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The matrix diophantine equations $AX+BY=C$

Karpatsʹkì Matematičnì Publìkacìï, 2011
A method of constructing of solutions of matrix Diophantineequations $AX+BY=C$ over commutative domains of finitely generatedprincipal ideals is suggested. The formulas of general solutionsof such equations in some cases is proposed.
N. S. Dzhaliuk, V. M. Petrychkovych
doaj  

The approximate functional equation of some Diophantine series. [PDF]

Mon Hefte Math, 2023
Chamizo F, Martin B.
europepmc   +1 more source

An Extensive Review of the Literature Using the Diophantine Equations to Study Fuzzy Set Theory

International Journal of Mathematics and Mathematical Sciences
Every field in mathematics has made significant progress in research with fuzzy sets. Numerous application fields were discovered in both empirical and theoretical investigations, ranging from information technology to medical technology, from the ...
K. M. Abirami, Narayanan Veena, R. Srikanth, P. Dhanasekaran   +3 more
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