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2024 | OriginalPaper | Chapter

The Diophantine Equation \(x^2+5^a7^b11^c19^d=4y^n\)

Author : Nguyen Xuan Tho

Published in: Class Groups of Number Fields and Related Topics

Publisher: Springer Nature Singapore

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Abstract

The chapter delves into the Diophantine equation, specifically the Lebesgue-Ramanujan-Nagell equation, which has a rich history and various solutions discovered by notable mathematicians. The author presents a main theorem that completely solves the equation under specific conditions, utilizing deep theorems on primitive divisors of Lucas sequences and computational methods. The chapter is structured with preliminaries, proofs of the main theorem, and several lemmas that tackle different cases of the equation. The use of MAGMA software for computations adds a modern twist to the traditional mathematical approach, making the solutions both rigorous and accessible.

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previous chapter On the Divisibilities , , and

next chapter A Brief Survey of Recent Results on Pólya Groups

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Title: The Diophantine Equation
Author: Nguyen Xuan Tho
Publisher: Springer Nature Singapore
Book: Class Groups of Number Fields and Related Topics
Print ISBN: 978-981-9769-10-0

Electronic ISBN: 978-981-9769-11-7

Copyright Year: 2024
DOI: https://doi.org/10.1007/978-981-97-6911-7_11

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