Results 31 to 40 of about 565 (158)

The Computing of Pythagoras Triples in Symbolic 2-Plithogenic Rings [PDF]

Neutrosophic Sets and Systems, 2023
This paper is dedicated to finding a general algorithm for generating different solutions for Pythagoras' non-linear Diophantine equation in four variables 𝑥 2 + 𝑦 2 = 𝑧 2 in symbolic 2-plithogenic rings, which are known as Pythagoras triples.
Abuobida Mohammed A. Alfahal, Yaser Ahmad Alhasan, Raja Abdullah Abdulfatah, Ahmad Abd Al-Aziz   +3 more
doaj  

Cryptography Using Linear Diophantine Equation

, 2022
: This study is focused on the encrypting and decrypting of messages using the Linear Diophantine Equation: where , that is the integers and are relatively prime.
Mark Kenneth C. Engcot
core   +1 more source

On Pythagoras Triples in Symbolic 3-Plithogenic Rings [PDF]

Neutrosophic Sets and Systems, 2023
The objective of this paper is to find necessary and sufficient conditions for a symbolic 3-plithogenic triple (𝑡0 + 𝑡1𝑃1 + 𝑡2𝑃2 + 𝑡3𝑃3, 𝑠0 + 𝑠1𝑃1 + 𝑠2𝑃2 + 𝑠3𝑃3, 𝑘0 + 𝑘1𝑃1 + 𝑘2𝑃2 + 𝑘3𝑃3 ) to be a Pythagoras triple, i.e.
Abuobida Mohammed A. Alfahal, Yaser Ahmad Alhasan, Raja Abdullah Abdulfatah, Noor Edin Rabeh   +3 more
doaj  

The Frobenius Number for Jacobsthal Triples Associated with Number of Solutions

Axioms, 2023
In this paper, we find a formula for the largest integer (p-Frobenius number) such that a linear equation of non-negative integer coefficients composed of a Jacobsthal triplet has at most p representations.
Takao Komatsu, Claudio Pita-Ruiz
doaj   +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
doaj   +1 more source

On the Conditions for Symbolic 3-Plithogenic Pythagoras Quadruples [PDF]

Neutrosophic Sets and Systems, 2023
The objective of this paper is to find the necessary and sufficient conditions for a symbolic 3-plithogenic quadruple (𝑡0 + 𝑡1𝑃1 + 𝑡2𝑃2 + 𝑡3𝑃3, 𝑠0 + 𝑠1𝑃1 + 𝑠2𝑃2 + 𝑠3𝑃3, 𝑘0 + 𝑘1𝑃1 + 𝑘2𝑃2 + 𝑘3𝑃3, 𝑙0 + 𝑙1𝑃1 + 𝑙2𝑃2 + 𝑙3𝑃3 ) to be a Pythagoras quadruple, i.e.
Abuobida Mohammed A. Alfahal, Yaser Ahmad Alhasan, Raja Abdullah Abdulfatah, Sara Sawalmeh   +3 more
doaj  

Small solutions of linear Diophantine equations

Discrete Mathematics, 1986
Given a system of linear diophantine equations and let (*) \(Ax=B\) be its matrix form, where \(A=(a_{ij})\) is a \(m\times n\), \(x=(x_k)\) and \(B=(a_{k,n+1})\) are \(m\times 1\) matrices. Further, given integers \(1\leq j_1< \cdots < j_m\leq n+1\), let \(d_{j_1,\ldots, j_m} = \det (a_{i,j_r}),\) \(1\leq i,r\leq m\), \(X=\sup \{| d_{j_1,\ldots, j_m}|:
I. Borosh, M. Flahive, B. Treybig
openaire   +1 more source

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
doaj   +1 more source

Geometry of the Minimal Solutions of a Linear Diophantine Equation [PDF]

SIAM Journal on Discrete Mathematics, 2021
12 pages; To appear in SIAM J.
openaire   +2 more sources

Spectrum sensing based on high/low sensing times

e-Prime: Advances in Electrical Engineering, Electronics and Energy, 2023
Cognitive Radio spectrum sensing is one of the important technique to utilize the unused specturm for secondary user signal transmission without interference with the primary users of the spectrum.
Ramamurthy Garimella, Jagannadha Swamy Tata   +1 more
doaj   +1 more source