Elementary number theory

Author: Shan Zun
Publisher:
Publish Date: 2009-05-04
Features: This textbook series is designed with the aim of fully implementing the educational policies of the Party and comprehensively improving the quality of education. It takes the principle of "education should be oriented towards modernization, the world, and the future" as its guide, and is based on the "Plan," reflecting the ideas of quality-oriented education and reform and innovation. It embodies the intrinsic requirements of university-level education and serving primary school education, follows the developmental patterns of primary school teachers and the characteristics of subject teaching, strengthens general education, emphasizes the integration of humanities and sciences, and intensifies the cultivation of professional abilities. The educational structure is well-organized, and the textbook system is scientifically constructed. During the writing process, the teaching experiences of experimental schools within and outside the province were fully absorbed, and advanced achievements in the reform of teacher education were learned from internationally. On the premise of ensuring scientificity, the timeliness, relevance, and systematic nature of the textbook content are further highlighted. It adheres to the unity of teacher education and academic rigor, balances foundational and developmental aspects, making the textbook system more aligned with the needs of cultivating primary school teachers with bachelor's or associate degrees for the 21st century. The entire series is compiled according to the goal of overall planning, phased implementation, and gradual implementation. This textbook series is suitable for full-time schools that train primary school teachers with bachelor's or associate degrees, as well as for in-service primary school teachers seeking further education, continuing education, and self-study examinations. It is a textbook for the associate degree program in normal schools. Number theory, the study of numbers (especially integers), is also known as arithmetic or higher arithmetic, and has many applications in secondary and primary school teaching. Therefore, it is necessary for students in normal schools to study it. This textbook is characterized by being concise and practical. The content is divided into five chapters: divisibility of numbers, congruences, number-theoretic functions, indeterminate equations, and continued fractions. Each chapter is closely related to secondary and primary school mathematics. Pure theoretical issues, such as Peano's ordinal theory, are not included in the book because they are of limited practical use. Each chapter provides a brief introduction to essential knowledge and is supplemented with numerous examples to help students apply the relevant knowledge. Practice has shown that the main difficulty students face in learning number theory is not in acquiring the knowledge but in applying it to solve problems. Therefore, the focus is placed on the latter. Additionally, selected exercises are included to help students consolidate their knowledge. Some exercises marked with an asterisk are more challenging and are suitable for students with better performance to enhance their creative abilities. Solutions or hints are provided for all exercises for reference by teachers.