Let $I(a,b,m)$ be the smallest postive integer solution $x$ to the modular equation $ax\equiv b\mod m.$ What is the quickest way to find $I(a,b,m)$ for given integers $a,b,m$?
I know how to find it with the generalized euclidean algorithm, but is that the quickest way? Also, are there any curious properties of $I(a,b,m)$ like efficient bounds or identities?