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Linear Diophantine equations and congruences [PDF]
This bachelor's thesis summarizes and systematizes knowledge about congruences and linear Diophantine equations. This work is divided into two parts. The first part is dedicated to congruences.
Kaňáková, Natálie
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Diophantine Equations Related to Linear Recurrence Sequences [PDF]
The aim of this dissertation is to investigate the solutions of some Diophantine equations connected to linear recurrence sequences. We firstly study the integer solutions of Diophantine equations related to reciprocals and repdigits with linear ...
Hashim, Hayder Raheem
core
SOLUTIONS OF SOME LINEAR DIOPHANTINE EQUATIONS [PDF]
This paper concerns with the problem of obtaining solutions of some linear Diophantine ...
P. Reka
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A Study of Symbolic 2-Plithogenic Split-Complex Linear Diophantine Equations in Two Variables [PDF]
The equation 𝐴𝑋 + 𝐵𝑌 = 𝐶 is called symbolic 2-plithogenic linear Diophantine equation with two variables if 𝐴, 𝐵, 𝑋, 𝑌, 𝐶 are symbolic 2-plithogenic split-complex integers.
Rama Asad Nadweh +3 more
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Elementary Deduction Problem for Locally Stable Theories with Normal Forms [PDF]
We present an algorithm to decide the intruder deduction problem (IDP) for a class of locally stable theories enriched with normal forms. Our result relies on a new and efficient algorithm to solve a restricted case of higher-order associative ...
Mauricio Ayala-Rincón +2 more
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The Mathematical Safe Problem and Its Solution (Part 2)
Introduction. The problem of mathematical safe arises in the theory of computer games and cryptographic applications. The article considers numerous variations of the mathematical safe problem and examples of its solution using systems of linear ...
Sergii Kryvyi, Hryhorii Hoherchak
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Diophantine Equations Related with Linear Binary Recurrences
Summary: In this paper we find all solutions of four kinds of the Diophantine equations \[ x^2 \pm V_t xy-y^2 \pm x=0 \text{ and } x^2 \pm V_txy-y^2 \pm y=0, \] for an odd number \(t\), and, \[ x^2 \pm V_txy+y^2-x=0 \text{ and } x^2 \pm V_txy+y^2-y=0, \] for an even number \(t\), where \(V_n\) is a generalized Lucas number.
Kilic, Emrah, Akkus, Ilker, Omur, Nese
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On a few Diophantine equations, in particular, Fermat's last theorem
This is a survey on Diophantine equations, with the purpose being to give the flavour of some known results on the subject and to describe a few open problems.
C. Levesque
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Mulatu Numbers Which Are Concatenation of Two Fibonacci Numbers
Let (M_k) be the sequence of Mulatu numbers defined by M_0=4, M_1=1, M_k=M_(k-1)+M_(k-2) and (F_k) be the Fibonacci sequence given by the recurrence F_k=F_(k-1)+F_(k-2) with the initial conditions F_0=0, F_1=1 for k≥2.
Fatih Erduvan, Merve Güney Duman
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Non-Linear Diophantine Equation
This paper is an important study about these Non-Linear Equation which have integer solution exists. i.e., Non-Linear Diophantine Equation, which have named by the famous Greek Mathematician Diophantus of Alexandria. In this paper we have focused to solve Non-Linear Diophantine Equations.
Jeetendra kumar -, S. N. Adhikary -
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