Modular Inverse

A modular inverse is a number that, when multiplied by another number within a specific modular system (like clock arithmetic), equals 1. Imagine you’re working with a clock of a certain size; the modular inverse of a number is what you need to multiply by that number to return to 1 on the clock. For example, in modulo 7 arithmetic, the modular inverse of 3 is 5 because 3 × 5 = 15, and 15 mod 7 equals 1. It’s essential in fields like cryptography for solving equations where numbers are reused within a set range.