Theoretical and Natural Science
- The Open Access Proceedings Series for Conferences
Theoretical and Natural Science
Vol. 25, 20 December 2023
Open
Access | Article
The development of P-adic numbers theoretically and their use in number theory
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Abstract
Stemming from the need to formalize the divisibility of rational numbers, p-adics provide a unique mathematical perspective rooted in prime number theory. This article provides a comprehensive discussion of p-adic numbers, including their research background, definition, properties, theory, and extensions. This study first elucidates the historical background and significance of p-adic numbers, emphasizing their key role in number theory and its applications. At the heart of this research is a deep dive into the precise definition of p-radical numbers, revealing their unique, often counterintuitive, distance measure. We look at their fundamental characteristics, demonstrate their illogical characteristics, and discuss how they affect transcendental number theory, Diophantine equations, and algebraic number theory. Furthermore, this article explores the theoretical foundations of p-radical numbers and their extensions, emphasizing their integral role in advanced mathematical structures such as p-radical analysis and p-radical geometry. By covering these aspects, this study aims to highlight the lasting impact of p-adic on modern mathematics, reshape our understanding of divisibility, and advance mathematical inquiry into new and uncharted territory.
Keywords
p-adic number, prime, number theory
References
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Data Availability
The datasets used and/or analyzed during the current study will be available from the authors upon reasonable request.
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- Volume Title
- Proceedings of the 3rd International Conference on Computing Innovation and Applied Physics
- ISBN (Print)
- 978-1-83558-233-6
- ISBN (Online)
- 978-1-83558-234-3
- Published Date
- 20 December 2023
- Series
- Theoretical and Natural Science
- ISSN (Print)
- 2753-8818
- ISSN (Online)
- 2753-8826
- DOI
- 10.54254/2753-8818/25/20240919
- Copyright
- 20 December 2023
- Open Access
- This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited