X-Nico

Secret sharing using the Chinese remainder theorem

By Bézout's identity, since $(m\; i,M/m\; i)\; =\; 1$, there exist positive integers $r\; i$ and $s\; i$, that can be found using the Extended Euclidean algorithm, such that $r\; i.m\; i+s\; i.M/m\; i\; =\; 1$.

see also