Number theory is a branch of mathematics, which mainly studies the properties of integers and their relationships with other mathematical objects. The basic knowledge of number theory includes the following aspects:

1. Integer concept: Integer is a numerical value without decimal part, including positive integer, negative integer and zero. Integers play an important role in number theory because they constitute the basic elements of real number sets.

2. Prime numbers and composite numbers: Prime numbers refer to integers greater than 1 that can only be divisible by 1 and itself, such as 2, 3 and 5. A composite number refers to an integer with other factors besides 1 and itself, such as 4, 6, 8, etc. Prime numbers have a special position in number theory, because they are the basic elements of other integers.

3. Factorization: Factorization is the process of representing an integer as the product of several prime numbers. For example, 28 is decomposed into 2×2×7. Factorization is of great significance in number theory, because it helps us to understand the nature and structure of integers.

4. Maximum common divisor and minimum common multiple: the maximum common divisor (GCD) refers to the maximum factor * * * shared by two or more integers, for example, the maximum common divisor of 12 and 16 is 4. The least common multiple (LCM) refers to the least common multiple of two or more integers. For example, the least common multiple of 12 and 16 is 48. The greatest common divisor and the least common multiple are widely used in number theory, such as solving practical problems and optimizing algorithms.

5. Congruence and modular operation: Congruence refers to the remainder after division of two integers. For example, the remainder after dividing 7 by 3 is 1. Modular operation refers to the process of taking the remainder after dividing an integer, for example, 7mod3 is equal to 1. Congruence and modular operations are of great significance in number theory, because they help us to study the properties and structure of integers.

6. Fermat's Last Theorem: Fermat's Last Theorem is a theorem about prime numbers. It points out that if P is a prime number and A is an arbitrary positive integer less than P, then the power of A minus A is a multiple of P. Fermat's Last Theorem has important applications in cryptography and computer science.

7. Euler function and euler theorem: Euler function φ(n) refers to the number of positive integers less than n and coprime with n, and euler theorem is a theorem about the distribution of prime numbers. It is pointed out that for any integer n greater than 1, its Euler function φ(n) can be expressed as the sum of the indices of all different prime factors in the form of positive integers of n, and Euler function and euler theorem are of great significance in number theory, because they are helpful for us to study the properties and properties of prime numbers.