Results 21 to 30 of about 1,143,114 (202)

The integer solutions of the cubic Diophantine equation x3±33=pqy2

Xi'an Gongcheng Daxue xuebao, 2021
The solvability of a class of cubic Diophantine equations is studied by using properties of congruence, Legendre symbol and the methods of elementary number theory.
Heng LI, Hai YANG, Yongliang LUO
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On Some Algorithms for Solving Different Types of Symbolic 2-Plithogenic Algebraic Equations [PDF]

Neutrosophic Sets and Systems, 2023
The main goal of this paper is to study three different types of algebraic symbolic 2-plithogenic equations. The symbolic 2-plithogenic linear Diophantine equations, symbolic 2-plithogenic quadratic equations, and linear system of symbolic 2-plithgenic ...
Ahmad Khaldi, Khadija Ben Othman, Oliver Von Shtawzen, Rozina Ali, Sarah Jalal Mosa   +4 more
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On the solution of the exponential Diophantine equation 2x+m2y=z2, for any positive integer m [PDF]

Journal of Hyperstructures, 2023
It is well known that the exponential Diophantine equation 2x+ 1=z2 has the unique solution x=3 and z=3 innon-negative integers, which is closely related to the Catlan's conjecture.
Mridul Dutta, Padma Bhushan Borah
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Gaussian Integer Solutions of the Diophantine Equation x^4+y^4=z^3 for x≠ y

مجلة بغداد للعلوم, 2023
The investigation of determining solutions for the Diophantine equation  over the Gaussian integer ring for the specific case of  is discussed.
Shahrina Ismail , Kamel Ariffin Mohd Atan , Diego Sejas Viscarra , Kai Siong Yow   +3 more
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Three Diophantine equations concerning the polygonal numbers [PDF]

Notes on Number Theory and Discrete Mathematics
Many 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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Modified Block Homotopy Perturbation Method for solving triangular linear Diophantine fuzzy system of equations

Advances in Mechanical Engineering, 2023
Numerous real-world applications can be solved using the broadly adopted notions of intuitionistic fuzzy sets, Pythagorean fuzzy sets, and q-rung orthopair fuzzy sets.
Mudassir Shams, Nasreen Kausar, Naveed Khan, Mohd Asif Shah   +3 more
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On special exponential Diophantine equations [PDF]

Notes on Number Theory and Discrete Mathematics, 2023
In this paper, we will focus on the study of a special type of exponential Diophantine equations, including a proof. The main contribution of this article is the mentioned type of equations, which can only be solved by the methods of elementary ...
Tomáš Riemel
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On a Diophantine Equation [PDF]

Journal of the London Mathematical Society, 1951
Summary: Denote by \(N(a,b)\) the smallest integer \(n\) so that \[ \frac{a}{b}=\frac{1}{x_1}+\cdots+\frac{1}{x_n},\quad ...
openaire   +4 more sources

GEOMETRIC THEOREMS, DIOPHANTINE EQUATIONS, AND ARITHMETIC FUNCTIONS [PDF]

, 2002
This book contains short notes or articles, as well as studies on several topics of Geometry and Number theory. The material is divided into ve chapters: Geometric theorems; Diophantine equations; Arithmetic functions; Divisibility properties of numbers ...
Sándor, József
core   +1 more source

Application of the group action approach to solving linear Diophantine equations [PDF]

Известия Саратовского университета. Новая серия: Математика. Механика. Информатика
The 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, Tsybulya, Liliya Mikhailovna   +1 more
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