Results 41 to 50 of about 1,224,172 (204)

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 note on the Diophantine equation (xᵏ-1)(yᵏ-1)²=zᵏ-1 [PDF]

Notes on Number Theory and Discrete Mathematics
We prove that, for k≥10, the Diophantine equation (xᵏ-1)(yᵏ-1)²=zᵏ-1 in positive integers x, y, z, k with z>1, has no solutions satisfying ...
Yangcheng Li
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An Introduction to Refined Neutrosophic Number Theory [PDF]

Neutrosophic Sets and Systems, 2021
Number theory is concerned with properties of integers and Diophantine equations. The objective of this paper is dedicated to introduce the basic concepts in refined neutrosophic number theory such as division, divisors, congruencies, and Pell's equation
Mohammad Abobala, Muritala Ibrahim
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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 \(x=2^m\).
openaire   +3 more sources

Generating Pythagoras Quadruples in Symbolic 2-Plithogenic Commutative Rings [PDF]

Neutrosophic Sets and Systems, 2023
This paper is dedicated to find a general algorithm for generating different solutions for Pythagoras non-linear Diophantine equation .
Yaser Ahmad Alhasan, Abuobida Mohammed A. Alfahal, Raja Abdullah Abdulfatah   +2 more
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A brief survey on the generalized Lebesgue-Ramanujan-Nagell equation [PDF]

Surveys in Mathematics and its Applications, 2020
The generalized Lebesgue-Ramanujan-Nagell equation is an important type of polynomial-exponential Diophantine equation in number theory. In this survey, the recent results and some unsolved problems of this equation are given.
Maohua Le, Gökhan Soydan
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On 1w+1x+1y+1z=12 $\frac{1}{w} + \frac{1}{x} + \frac{1}{y} + \frac{1}{z} = \frac{1}{ 2} $ and some of its generalizations

Journal of Inequalities and Applications, 2018
In this paper, we give a straightforward approach to obtaining the solution of the Diophantine equation 1w+1x+1y+1z=12 $\frac{1}{w} + \frac{1}{x} + \frac{1}{y} + \frac{1}{z} = \frac{1}{2}$. We also establish that the Diophantine equation 1w+1x+1y+1z=mn $\
Tingting Bai
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On the Symbolic 2-plithogenic Fermat's Non-Linear Diophantine Equation [PDF]

Neutrosophic Sets and Systems, 2023
This paper is dedicated to find all symbolic 2-plithogenic integer solutions for the symbolic 2-plithogenic Fermat's Diophantine equation.
Heba Alrawashdeh, Othman Al-Basheer, Arwa Hajjari   +2 more
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Studies of Positive Integer Solutions of the Diophantine Equation x2−ay2−bx−cy−d=0 by the Transformation Method

Journal of Mathematics
Solving the Diophantine equation has fascinated mathematicians from various civilizations. In this paper, we propose the resolution of quadratic Diophantine equations with integer coefficients.
Francklin Fenolahy, Harrimann Ramanantsoa, André Totohasina   +2 more
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The diophantine equation r2+r(x+y)=kxy

International Journal of Mathematics and Mathematical Sciences, 1985
The Diophantine equation of the title is solved in integers.
W. R. Utz
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