Modular arithmetic is a mathematical system that deals with remainders and is used in various branches of mathematics, such as number theory, algebra, and cryptography. It is often referred to as clock arithmetic, residue arithmetic, or simply modulus arithmetic. In this system, numbers wrap around cyclically, which means that any number is equivalent to another number that differs by a multiple of a given integer called the modulus. Other synonyms for modular arithmetic include finite field arithmetic, Galois arithmetic, and cyclic group arithmetic. These terms refer to more advanced concepts within modular arithmetic and are often used in research and specialized fields of mathematics.