Results 31 to 40 of about 3,530,646 (225)

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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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
doaj  

A diophantine equation [PDF]

Glasgow Mathematical Journal, 1985
I was recently challenged to find all the cases when the sum of three consecutive integral cubes is a square; that is to find all integral solutions x, y ofy2=(x−1)3+x3+(x+1)3=3x(x2+2)This is an example of a curve of genus 1. There is an effective procedure for finding all integral points on a given curve of genus 1 ([1, Theorem 4.2], [2]): that is, it
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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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On primitive integer solutions of the Diophantine equation $t^2=G(x,y,z)$ and related results

, 2015
In this paper we investigate Diophantine equations of the form $T^2=G(\overline{X}),\; \overline{X}=(X_{1},\ldots,X_{m})$, where $m=3$ or $m=4$ and $G$ is specific homogenous quintic form. First, we prove that if $F(x,y,z)=x^2+y^2+az^2+bxy+cyz+dxz\in\Z[x,
Gawron, Maciej, Ulas, Maciej
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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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Random Diophantine equations, I

Advances in Mathematics, 2014
Comment: The results in this paper use an $L^2$-technique and supersede those in an earlier version (see arXiv:1110.3496) that relied on an $L^1$-argument, but for instructional purposes we found it useful to keep the older, technically simpler version.
Brüdern, Jörg, Dietmann, Rainer
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