Relevant bibliographies by topics / Diophantine equation

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Diophantine equation'

Author: Grafiati
Published: 4 June 2021
Last updated: 25 July 2025

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Journal articles on the topic "Diophantine equation"

1

G, Janaki, and Gowri Shankari A. "(Exponential Diophantine Equation n2􀀀1 )u +n2v = w2;n = 2;3;4;5." Indian Journal of Science and Technology 17, no. 2 (2024): 166–70. https://doi.org/10.17485/IJST/v17i2.2544.

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Abstract <strong>Objectives:</strong>&nbsp;Diophantine research focuses on various ways to tackle multivariable and multidegree Diophantine problems. A Diophantine equation is a polynomial equation with only integer solutions. The objective of this manuscript is to find the solutions to a few exponential Diophantine equations and . Also generalize the Exponential equation , and of the form and explore that it has at least one solution as .<strong>&nbsp;Methods:</strong>&nbsp;Diophantine equations may have finite, infinite or no solutions in integers. There is no universal method for finding so
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Sankari, Hasan, and Mohammad Abobala. "On The Group of Units Classification In 3-Cyclic and 4-cyclic Refined Rings of Integers And The Proof of Von Shtawzens' Conjectures." International Journal of Neutrosophic Science 21, no. 4 (2023): 146–54. http://dx.doi.org/10.54216/ijns.210414.

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First Von Shtawzen's Diophantine equation is a non-linear Diophantine equation with three variables . This equation has been conjectured that it has a finite number of integer solutions, and this number of solutions is divisible by 6. Second Von Shtawzen's Diophantine equation is a non-linear Diophantine equation with four variables. This equation has been conjectured that it has a finite number of integer solutions, and this number of solutions is divisible by 8. In this paper, we prove that first Von Shtawzen's conjecture is true, where we show that first Von Shtawzen's Diophantine equations
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Aggarwal, S., and S. Kumar. "On the Exponential Diophantine Equation (132m) + (6r + 1)n = z2." Journal of Scientific Research 13, no. 3 (2021): 845–49. http://dx.doi.org/10.3329/jsr.v13i3.52611.

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Nowadays, mathematicians are very interested in discovering new and advanced methods for determining the solution of Diophantine equations. Diophantine equations are those equations that have more unknowns than equations. Diophantine equations appear in astronomy, cryptography, abstract algebra, coordinate geometry and trigonometry. Congruence theory plays an important role in finding the solution of some special type Diophantine equations. The absence of any generalized method, which can handle each Diophantine equation, is challenging for researchers. In the present paper, the authors have d
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Wu, Yi, and Zheng Ping Zhang. "The Positive Integer Solutions of a Diophantine Equation." Applied Mechanics and Materials 713-715 (January 2015): 1483–86. http://dx.doi.org/10.4028/www.scientific.net/amm.713-715.1483.

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In this paper, we studied the positive integer solutions of a typical Diophantine equation starting from two basic equations including a Diophantine equation and a Pell equation, and we will prove all the positive integer solutions of the typical Diophantine equation.
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Sathiyapriya, R., та M. A. Gopalan. "Homogeneous Quadratic Equation with Four Unknowns 𝑥2 + 𝑥𝑦 + 𝑦2 = 𝑧2 + 𝑧𝑤 + 𝑤2". Indian Journal Of Science And Technology 17, № 27 (2024): 2841–47. http://dx.doi.org/10.17485/ijst/v17i27.1710.

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Objectives: Diophantine research focuses on various ways to tackle multi variable and multi-degree Diophantine problems. A Diophantine equation is a polynomial equation with only integer solutions. The objective of this manuscript is to find the solutions to Polynomial Diophantine equation . Methods: Diophantine equations may have finite, infinite, or no solutions in integers. There is no universal method for finding solutions to Diophantine equations. Different choice of solutions in integers is obtained through using linear transformations and employing the factorization method. Findings: Ma
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R, Sathiyapriya, та A. Gopalan M. "Homogeneous Quadratic Equation with Four Unknowns 𝑥2 + 𝑥𝑦 + 𝑦2 = 𝑧2 + 𝑧𝑤 + 𝑤2". Indian Journal of Science and Technology 17, № 27 (2024): 2841–47. https://doi.org/10.17485/IJST/v17i27.1710.

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Abstract <strong>Objectives:</strong>&nbsp;Diophantine research focuses on various ways to tackle multi variable and multi-degree Diophantine problems. A Diophantine equation is a polynomial equation with only integer solutions. The objective of this manuscript is to find the solutions to Polynomial Diophantine equation .<strong>&nbsp;Methods:</strong>&nbsp;Diophantine equations may have finite, infinite, or no solutions in integers. There is no universal method for finding solutions to Diophantine equations. Different choice of solutions in integers is obtained through using linear transforma
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Kaleeswari, K., J. Kannan, A. Deepshika, and M. Mahalakshmi. "Computations of Exponential Diophantine Rectangles over Gnomonic Numbers using Python." Indian Journal Of Science And Technology 17, no. 42 (2024): 4449–53. http://dx.doi.org/10.17485/ijst/v17i42.3491.

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Objective: The main objective of this paper is to define and collect a new type of rectangle called the Exponential Diophantine Rectangle over Gnomonic numbers (figurate numbers that take the form 𝑛2 − (𝑛 − 1)2, 𝑛 ∈ 𝑁). Methods: It is done by solving the two exponential Diophantine equations using Mihailescu’s theorem, binomial expansion, and the basic theory of congruences. Findings: Here, it is proven that there are only four exponential Diophantine rectangles over Gnomonic numbers. Finally, it is validated using Python programming for a specific limit. Novelty: The concept of solving an exp
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Biswas, D. "Does the Solution to the Non-linear Diophantine Equation 3<sup>x</sup>+35<sup>y</sup>=Z<sup>2</sup> Exist?" Journal of Scientific Research 14, no. 3 (2022): 861–65. http://dx.doi.org/10.3329/jsr.v14i3.58535.

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This paper investigates the solutions (if any) of the Diophantine equation 3x + 35y = Z2, where , x, y, and z are whole numbers. Diophantine equations are drawing the attention of researchers in diversified fields over the years. These are equations that have more unknowns than a number of equations. Diophantine equations are found in cryptography, chemistry, trigonometry, astronomy, and abstract algebra. The absence of any generalized method by which each Diophantine equation can be solved is a challenge for researchers. In the present communication, it is found with the help of congruence th
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Chen, Imin. "A Diophantine Equation Associated to X0(5)." LMS Journal of Computation and Mathematics 8 (2005): 116–21. http://dx.doi.org/10.1112/s1461157000000929.

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AbstractSeveral classes of Fermat-type diophantine equations have been successfully resolved using the method of galois representations and modularity. In each case, it is possible to view the proper solutions to the diophantine equation in question as corresponding to suitably defined integral points on a modular curve of level divisible by 2 or 3. Motivated by this point of view, an example of a diophantine equation associated to the modular curve X0(5) is discussed in this paper. The diophantine equation has four terms rather than the usual three terms characteristic of generalized Fermat e
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Maran, A. K. "A Simple Solution for Diophantine Equations of Second, Third and Fourth Power." Mapana - Journal of Sciences 4, no. 1 (2005): 96–100. http://dx.doi.org/10.12723/mjs.6.17.

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We know already that the set Of positive integers, which are satisfying the Pythagoras equation Of three variables and four variables cre called Pythagorean triples and quadruples respectively. These cre Diophantine equation OF second power. The all unknowns in this Pythagorean equation have already Seen by mathematicians Euclid and Diophantine. Hcvwever the solution defined by Euclid are Diophantine is also again having unknowns. The only to solve the Diophantine equations wos and error method. Moreover, the trial and error method to obtain these values are not so practical and easy especiall
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Dissertations / Theses on the topic "Diophantine equation"

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Bartolomé, Boris. "Diophantine equations and cyclotomic fields." Thesis, Bordeaux, 2015. http://www.theses.fr/2015BORD0104/document.

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Cette thèse examine quelques approches aux équations diophantiennes, en particulier les connexions entre l’analyse diophantienne et la théorie des corps cyclotomiques.Tout d’abord, nous proposons une introduction très sommaire et rapide aux méthodes d’analyse diophantienne que nous avons utilisées dans notre travail de recherche. Nous rappelons la notion de hauteur et présentons le PGCD logarithmique.Ensuite, nous attaquons une conjecture, formulée par Skolem en 1937, sur une équation diophantienne exponentielle. Pour cette conjecture, soit K un corps de nombres, α1 ,…, αm , λ1 ,…, λm des élém
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Ren, Ai. "Embedded Surface Attack on Multivariate Public Key Cryptosystems from Diophantine Equation." University of Cincinnati / OhioLINK, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1558364211159262.

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Weeman, Glenn Steven. "A Diophantine Equation for the Order of Certain Finite Perfect Groups." University of Akron / OhioLINK, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=akron1396902470.

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Rahimi, Shahriar. "A NOVEL LINEAR DIOPHANTINE EQUATION-BAESD LOW DIAMETER STRUCTURED PEER-TO-PEER NETWORK." OpenSIUC, 2017. https://opensiuc.lib.siu.edu/dissertations/1462.

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This research focuses on introducing a novel concept to design a scalable, hierarchical interest-based overlay Peer-to-Peer (P2P) system. We have used Linear Diophantine Equation (LDE) as the mathematical base to realize the architecture. Note that all existing structured approaches use Distributed Hash Tables (DHT) and Secure Hash Algorithm (SHA) to realize their architectures. Use of LDE in designing P2P architecture is a completely new idea; it does not exist in the literature to the best of our knowledge. We have shown how the proposed LDE-based architecture outperforms some of the most we
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Smith, Jason. "Solvability characterizations of Pell like equations." [Boise, Idaho] : Boise State University, 2009. http://scholarworks.boisestate.edu/td/55/.

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Синиця, О. "Методи розв'язування діофантових рівнянь". Thesis, Cумський державний університет, 2016. http://essuir.sumdu.edu.ua/handle/123456789/48885.

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Розв’язок рівнянь в цілих числах є однією з стародавніх математичних задач. Основне джерело, яке дійшло до наших часів – видання праці Діофанта «Арифметика». На жаль, з тринадцяти книг, що входили до цього видання, тільки шість збереглися до Середніх віків, саме вони і стали джерелом натхнення для багатьох математиків.
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Maximenko, Marianna. "Contribution au calcul de la solution générale d'équations en mots." Rouen, 1995. http://www.theses.fr/1995ROUE5003.

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Le problème central de la thèse est d'effectuer les recherches du calcul de la solution générale d'équations en mots, donnée sous la forme d'un ensemble fini de collections paramétrées de solutions. Ce projet a été proposé par G. S. Makanin. Nous avons proposé dans ce travail un algorithme quasi linéaire du calcul de la solution générale de l'équation en mots à une variable avec des coefficients. Nous avons décrit la solution générale de l'équation miroir sous la forme des mots à vecteurs. En introduisant la notion d'invariant de Makanin, nous avons obtenu la caractéristique du graphe de l'équ
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Валенкевич, М. Є. "Діофантові рівняння". Thesis, Сумський державний університет, 2014. http://essuir.sumdu.edu.ua/handle/123456789/38857.

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Wellstead, Kevin. "Robust polynomial controller design." Thesis, Brunel University, 1991. http://bura.brunel.ac.uk/handle/2438/4866.

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The work presented in this thesis was motivated by the desire to establish an alternative approach to the design of robust polynomial controllers. The procedure of pole-placement forms the basis of the design and for polynomial systems this generally involves the solution of a diophantine equation. This equation has many possible solutions which leads directly to the idea of determining the most appropriate solution for improved performance robustness. A thorough review of many of the aspects of the diophantine equation is presented, which helps to gain an understanding of this extremely impor
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Опарій, О. С. "Застосування генетичного алгоритму до розв'язання діафантових рівнянь". Thesis, Сумський державний університет, 2013. http://essuir.sumdu.edu.ua/handle/123456789/40956.

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У даній роботі розглядається застосування генетичного алгоритму до розв’язання діафантового рівняння першого порядку. Генетичні алгоритми є потужним обчислювальним засобом для різних оптимізаційних задач. Ці алгоритми застосовуються у найрізноманітніших галузях: економіці, фізиці, технічних науках і т.п.
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Books on the topic "Diophantine equation"

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C, Williams Hugh, ed. Solving the Pell equation. Springer, 2009.

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Schmidt, Wolfgang M. Diophantine Approximations and Diophantine Equations. Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/bfb0098246.

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Schmidt, Wolfgang M. Diophantine approximations and diophantine equations. Springer, 1996.

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Padmanabha Rao, Anantapur, editor, translator, Bhāskarācārya 1114-, Bhāskarācārya 1114-, Gaṇeśadaivajña active 1520-1554 та Chinmaya International Foundation Shodha Sansthan, ред. Bhāskarācārya's Līlāvatī: Geometry, first degree indeterminate equation and permutations : a translation from Sanskrit into English with Sanskrit text and roman transliteration : with word by word meaning in the English text order of 138 ślokas and Gaṇeśadaivajña's the Buddhivilāsinī commentary. Chinmaya International Foundation Shodha Sansthan, 2015.

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Andreescu, Titu, and Dorin Andrica. Quadratic Diophantine Equations. Springer New York, 2015. http://dx.doi.org/10.1007/978-0-387-54109-9.

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Sprindžuk, Vladimir G. Classical Diophantine Equations. Edited by Ross Talent. Springer Berlin Heidelberg, 1993. http://dx.doi.org/10.1007/bfb0073786.

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Shorey, T. N. Exponential diophantine equations. Cambridge University Press, 2008.

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Sprindzhuk, V. G. Classical diophantine equations. Springer-Verlag, 1993.

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R, Tijdeman, ed. Exponential diophantine equations. Cambridge University Press, 1986.

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Grechuk, Bogdan. Polynomial Diophantine Equations. Springer International Publishing, 2024. http://dx.doi.org/10.1007/978-3-031-62949-5.

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Book chapters on the topic "Diophantine equation"

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Elliott, P. D. T. A. "A Diophantine Equation." In Grundlehren der mathematischen Wissenschaften. Springer New York, 1985. http://dx.doi.org/10.1007/978-1-4613-8548-6_3.

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Zannier, Umberto. "The S-unit equation." In Lecture Notes on Diophantine Analysis. Scuola Normale Superiore, 2014. http://dx.doi.org/10.1007/978-88-7642-517-2_5.

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Bombieri, E. "On the thue-mahler equation." In Diophantine Approximation and Transcendence Theory. Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/bfb0078711.

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Loeb, Arthur L. "A Diophantine Equation and its Solutions." In Concepts & Images. Birkhäuser Boston, 1993. http://dx.doi.org/10.1007/978-1-4612-0343-8_6.

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Křížek, Michal, Florian Luca, and Lawrence Somer. "Fermat Primes and a Diophantine Equation." In 17 Lectures on Fermat Numbers. Springer New York, 2002. http://dx.doi.org/10.1007/978-0-387-21850-2_11.

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Stoll, Michael. "How to Solve a Diophantine Equation." In An Invitation to Mathematics. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-19533-4_2.

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Shorey, T. N. "An Equation of Goormaghtigh and Diophantine Approximations." In Current Trends in Number Theory. Hindustan Book Agency, 2002. http://dx.doi.org/10.1007/978-93-86279-09-5_19.

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Jahnel, Jörg. "The Diophantine equation 𝑥⁴+2𝑦⁴=𝑧⁴+4𝑤⁴." In Mathematical Surveys and Monographs. American Mathematical Society, 2014. http://dx.doi.org/10.1090/surv/198/06.

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Hilbert, David. "The Diophantine Equation αm + βm + γm = 0." In The Theory of Algebraic Number Fields. Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/978-3-662-03545-0_36.

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Pethö, Attila. "On the solution of the diophantine equation Gn=pz." In EUROCAL '85. Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/3-540-15984-3_320.

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Conference papers on the topic "Diophantine equation"

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Medvid, Vladimir. "LINEAR DIOPHANTINE EQUATIONS ABOUT N UNKNOWNS." In 17th annual International Conference of Education, Research and Innovation. IATED, 2024. https://doi.org/10.21125/iceri.2024.0446.

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Algareeb, Eman Talib, and Valeriy Osipovich Osipyan. "A Mathematical Model of Asymmetric Encryption Based on Linear Diophantine Equations." In 2024 International Conference on Electrical, Computer and Energy Technologies (ICECET). IEEE, 2024. http://dx.doi.org/10.1109/icecet61485.2024.10697990.

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Zahari, N. M., S. H. Sapar, and K. A. Mohd Atan. "On the Diophantine equation." In PROCEEDINGS OF THE 20TH NATIONAL SYMPOSIUM ON MATHEMATICAL SCIENCES: Research in Mathematical Sciences: A Catalyst for Creativity and Innovation. AIP, 2013. http://dx.doi.org/10.1063/1.4801234.

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Avdyev, M. "THE DIOPHANTINE EQUATION FROM THE EYE OF PHYSICIST." In X Международная научно-практическая конференция "Культура, наука, образование: проблемы и перспективы". Нижневартовский государственный университет, 2022. http://dx.doi.org/10.36906/ksp-2022/57.

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A Diophantine equation is an equation with integer coefficients, the solutions of which must be found among integers. The equation is named after the mathematician Diophantus of Alexandria (III century). Despite its simplicity, a Diophantine equation may have a nontrivial solution (several solutions) or has no solution at all. Fermat's Last Theorem and Pythagorean Theorem are the Diophantine equations too. In 1900 The German mathematician David Hilbert formulated the Tenth problem. After 70 years, the answer turned out to be negative: there is no general algorithm. Nevertheless, for some cases
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ȚARĂLUNGĂ, Boris. "About solutions of some non – linear Diophantine equations." In Ştiință și educație: noi abordări și perspective. "Ion Creanga" State Pedagogical University, 2023. http://dx.doi.org/10.46727/c.v3.24-25-03-2023.p293-298.

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In this paper, it is show that the Diophantine exponential equation:2^x +12^y=z^2 has exactly three non – negative integer solutions {(3,0,3),(2,1,4),(8,2,20)}, the Diophantine exponential equation: 2^x+14^y=z^2 has exactly three non–negative integer solutions: {(3,0,3), (1,1,4),(7,2,18)}, the Diophantine exponential equation: 2^x+15^y=z^2 has exactly two non–negative integer solutions: {(3,0,3), (6,2,17)}.
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Medviď, Vladimir. "ALGORITHMS OF SOLVING THE DIOPHANTINE EQUATION." In 16th annual International Conference of Education, Research and Innovation. IATED, 2023. http://dx.doi.org/10.21125/iceri.2023.0225.

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He Kong, Bin Zhou, and Mao-Rui Zhang. "A Stein equation approach for solutions to the Diophantine equations." In 2010 Chinese Control and Decision Conference (CCDC). IEEE, 2010. http://dx.doi.org/10.1109/ccdc.2010.5498658.

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Özkoç, Arzu, Ahmet Tekcan, Theodore E. Simos, George Psihoyios, Ch Tsitouras, and Zacharias Anastassi. "Integer Solutions of a Special Diophantine Equation." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: International Conference on Numerical Analysis and Applied Mathematics. AIP, 2011. http://dx.doi.org/10.1063/1.3637759.

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Balfaqih, Abdulrahman, and Hailiza Kamarulhaili. "On the Diophantine equation x1a+x2a+⋯+xma=pkyb." In PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON MATHEMATICAL SCIENCES AND TECHNOLOGY 2018 (MATHTECH2018): Innovative Technologies for Mathematics & Mathematics for Technological Innovation. AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5136367.

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Srivastava, Saurabh, Anuraag Misra, and V. S. Pandit. "Auto tuned PID controller design using Diophantine equation." In 2012 International Conference on Communications, Devices and Intelligent Systems (CODIS). IEEE, 2012. http://dx.doi.org/10.1109/codis.2012.6422246.

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Reports on the topic "Diophantine equation"

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Jain, Himanshu, Edmund M. Clarke, and Orna Grumberg. Efficient Craig Interpolation for Linear Diophantine (Dis)Equations and Linear Modular Equations. Defense Technical Information Center, 2008. http://dx.doi.org/10.21236/ada476801.

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Osipov, Gennadij Sergeevich, Natella Semenovna Vashakidze, and Galina Viktorovna Filippova. Fundamentals of solving linear Diophantine equations with two unknowns. Постулат, 2018. http://dx.doi.org/10.18411/postulat-2018-2-37.

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