I only left with one question: why do we create three c? I don't see any regards to the number of it in CRT and Gauss method. And don't feel strong connection of the number of c_iphers with _e (which is also 3). Does it only connected with the length of the _m_essage? So that longer the message we cipher, than more ciphers we need to use CRT? And how is it connected with the limitation that _m_essage can't be longer than modulus?

Thank you for wonderful explanation, useful links, and this additional coverage!