👉 Modular arithmetic, or mod math, is a system of arithmetic for integers where numbers "wrap around" after reaching a certain value, called the modulus. In this system, instead of counting on a linear sequence from 0 to N-1, as in regular arithmetic, numbers are reduced to their remainder when divided by the modulus. For example, in modulo 5 arithmetic (often denoted as ℤ₅), the number 7 would be treated as 2, because 7 divided by 5 leaves a remainder of 2. This concept is fundamental in various fields including cryptography, computer science, and number theory, where it simplifies calculations and helps in managing large numbers efficiently. Modular operations like addition, subtraction, multiplication, and division are defined in such a way that they respect this "wrap-around" property, making computations manageable and often more intuitive.
