Modular Division
Modular Division Modular division is a mathematical operation that involves dividing two integers under a specified modulus. It’s particularly useful in number theory, cryptography, and computer science. The goal is to find the remainder of the division (modulo) of one number by another. Definition Given three positive integers: $a, b$, and $m$, we want to compute $a/b$ under modulo $m$. In other words, we seek to find a number $c$ such that: $(b \cdot c) \mod m = a \mod m $ When Is Modular Division Defined? 1.Inverse Existence : Modular division is defined when the inverse of the divisor exists. The inverse of an integer $x$ is another integer $y$ such that $(x \cdot y) \mod m = 1$, where $m$ is the modulus. In other words, $x$ and $m$ must be co-prime (i.e., their greatest common divisor is 1). 2.Finding the Inverse : To compute modular division, we need to find the modular multiplicative inverse of $b$ under modulus $m$. If the inverse doesn’t exist (i.e., GCD(b, m) is not 1),