Hi can anyone say how do I prove CRT by the following isomorphism:
If n= (m1)(m2)...(mk) where each m is relatively prime in pairs, then there is an isomorphism from Zn to ( Zm1 + Zm2 + ... + Zmk). Zn is the integers modulo n.
all I can say is that since Mi's are relatively prime then gcd of each pair will be=1. that is we can write each pair as linear combination of k*Mi+t*Mj=1. but I dont know how to take this fact to prove this isomorphism relationship and furthermore how this isomorphism will prove Chinese remainder theorem.