Theoretical and Natural Science
- The Open Access Proceedings Series for Conferences
Theoretical and Natural Science
Vol. 5, 25 May 2023
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Group Theory in Number Theory
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Abstract
The theory of groups exists in many fields of mathematics and has made a great impact on many fields of mathematics. In this article, this paper first introduces the history of group theory and elementary number theory, and then lists the definitions of group, ring, field and the most basic prime and integer and divisor in number theory that need to be used in this article. Then from the definitions, step by step, Euler's theorem, Bézout's lemma, Wilson's theorem and Fermat's Little theorem in elementary number theory are proved by means of definitions of group theory, cyclic groups, and even polynomials over domains. Finally, some concluding remarks are made. Many number theory theorems can be proved directly by the method of group theory without the action of tricks in number theory. Number theory is the thinking of certain special groups (e.g., (Z,+),(Z,×)), so the methods of group theory work well inside number theory.
Keywords
Group theory, Number theory, Ring theory.
References
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- Volume Title
- Proceedings of the 2nd International Conference on Computing Innovation and Applied Physics (CONF-CIAP 2023)
- ISBN (Print)
- 978-1-915371-53-9
- ISBN (Online)
- 978-1-915371-54-6
- Published Date
- 25 May 2023
- Series
- Theoretical and Natural Science
- ISSN (Print)
- 2753-8818
- ISSN (Online)
- 2753-8826
- DOI
- 10.54254/2753-8818/5/20230254
- Copyright
- 25 May 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