Modular arithmetic is a system of arithmetic for integers where numbers “wrap around” when reaching a certain value, called the modulus. The modulus is typically a positive integer greater than 1. In modular arithmetic, we are not interested in the absolute value of the remainder, but only in the remainder itself.

For example, consider the following calculation in modulo 7 arithmetic:

10 ≡ 3 (mod 7)

This means that 10 and 3 have the same remainder when divided by 7. In other words, 10 and 3 are congruent modulo 7.

Modular arithmetic has many applications in mathematics, computer science, and cryptography. For example, it is used to implement hash functions, which are used to store and retrieve data efficiently. It is also used to design encryption algorithms, which are used to protect data from unauthorized access.