👉 Brass math, also known as modular arithmetic, is a system of arithmetic that "wraps around" after reaching a certain value, called the modulus. In this system, numbers are treated as if they cycle through a fixed set of integers, typically from 0 to modulus -1 (or less), with operations like addition, subtraction, multiplication, and division following specific rules. For example, in modulus 12, 5 + 7 = 12, which equals 0 (since 12 mod 12 = 0). This means that after reaching 12, the cycle resets to 0. Key concepts include properties like the distributive law (a(b + c) = ab + ac), the existence of additive and multiplicative inverses (except for 0 in modular division), and the use of congruences to describe relationships between numbers. Brass math is fundamental in computer science, cryptography, and number theory, enabling efficient problem-solving and secure data transmission through operations like modular exponentiation and hash functions.
