An integer function is a mathematical function that takes an integer as input and produces an integer as output. These functions can include operations like addition, subtraction, multiplication, and division, but they specifically focus on whole numbers without fractions or decimals. Common examples include the floor function, which rounds down to the nearest integer, and the ceiling function, which rounds up. Integer functions are often used in computer science and programming, particularly in algorithms that require counting or indexing. They help manage data structures like arrays and are essential in areas such as graph theory and number theory.