In mathematics, module is a common concept. Usually refers to the remainder of one number under another number, or it can refer to the equivalence of two numbers in the sense of a certain number. For example, 10 modulo 3 equals 1, because 10 is divided by 3 to get modulo 3 1, and modulo 3 equals 1, because 3 is divided by 2 to get 1, so 1. Modulus is not only an operational symbol, but also a mathematical relationship. It has important applications in many branches of mathematics, such as number theory, algebra, computer science and so on.

Modular computing is widely used in many fields. In cryptography, modular operation is widely used in RSA encryption algorithm, which can ensure the correctness and security of encryption and decryption. In computer science, modular operation can be used to divide data quickly, and modular operation can be used to compress and store big data. In algebra, modular operation is an important operation mode, which is widely used to construct and study algebraic structures, such as rings and fields. Therefore, mastering the basic concepts and operation rules of modular operation is of great significance for understanding various applications in mathematics and computer science.

There are many important mathematical theories and properties in modular operation. For example, modular operations have the basic properties of addition, multiplication, subtraction and division, and so do these operations in the modular sense. There is also the basic theorem of arithmetic module, which shows that in the sense of module, a number can be uniquely decomposed into the product of prime numbers, so that the solution of the module equation can be obtained. In addition, modular operations also have cyclic properties and can be used to construct algebraic structures with cyclic properties, such as permutation groups and cyclic groups. Therefore, the related properties of modular operation are the basis of some important problems in mathematics and computer science.