What is modular inverse?

A modular inverse of a number a(modulo m) is the integer a^-1, such that a * a^-1 is equivalent to 1 (modulo m). Every integer a, except 0, has an inverse (modulo p) where p is a prime number and the integer is not a multiple of p.

Using modular arithmetic, the modular inverse of an integer a can be represented as the fraction 1 / a just as it is done in real number arithmetic. The Euclidean algorithm is used to find the solution to an equation, ax + my = 1, if a and m are relatively prime by considering the equation modulo m.