Arithmetic functions are mathematical functions that take an integer as input and return a numerical value based on specific arithmetic properties. Common examples include the divisor function, which counts the number of divisors of an integer, and the Euler's totient function, which counts the integers up to a given integer that are coprime to it. These functions are essential in number theory and have applications in various fields, including cryptography. These functions can be expressed in different forms, such as additive functions, which satisfy the property f(m+n) = f(m) + f(n) for all integers m and n . Another type is multiplicative functions, where f(mn) = f(m)f(n) for coprime integers m and n . Understanding these functions helps in analyzing the structure of integers and their relationships.