The expression "a mod b" refers to the mathematical operation known as the modulus. It calculates the remainder when the integer a is divided by another integer b. For example, if a is 10 and b is 3, then 10 mod 3 equals 1, because 10 divided by 3 is 3 with a remainder of 1. This operation is useful in various fields, including computer science and cryptography. It helps in determining cycles, such as in clock arithmetic, where time wraps around after reaching a certain point. Understanding "a mod b" is essential for solving problems involving remainders and periodic patterns.