1. Fundamentals of number theory: number theory is a subject that studies the properties of integers, so number theory experts need to have a deep understanding of the properties and operation rules of integers.
2. Algebraic knowledge: The solution of algebraic equations is often involved in number theory, so it is necessary to master the basic knowledge and skills of algebra, such as factorization and polynomial theory.
3. Modular operation: Modular operation is an important tool in number theory, which is used to solve congruence equations and other problems. Number theory experts need to master the properties and calculation methods of modular operation skillfully.
4. Combinatorial Mathematics: Problems in number theory can often be transformed into combinatorial mathematics problems, so number theory experts need to have some knowledge of combinatorial mathematics, such as permutation and combination, graph theory and so on.
5. Discrete mathematics: Discrete mathematics is a discipline that studies discrete structures and their properties, which is closely related to number theory. Number theory experts need to master the basic concepts and methods of discrete mathematics, such as set theory and logical reasoning.
6. Algorithms and programming: number theory experts need to be able to design efficient algorithms to solve complex number theory problems, and be skilled in using programming languages to realize algorithms.
7. Abstract thinking ability: number theory problems are often abstract and complex, and number theory experts need to have strong abstract thinking ability, and can transform practical problems into mathematical models and solve them.
8. Mathematical proof ability: number theory experts need to have solid mathematical proof ability and be able to prove the theorems and properties of number theory through strict reasoning and argumentation.
9. Mathematical thinking method: number theory experts need to have flexible mathematical thinking methods and be able to solve problems from different angles and ideas, such as induction and induction.
10. continuous learning and innovation ability: number theory is a developing discipline, and number theory experts need to have the ability of continuous learning and innovation and constantly update their mathematical knowledge and skills.