Chinese remainder Theorem The system is X=a mod m X=a mod m2 X=a mod mr Assume that g.c. d (m; mi =1 for itj. The system has a unique solution modulo m, mChinese Remainder Theorem • The system is – x = a1 mod m1 – x = a2 mod m2 – …. – x = ar mod mr – Assume that g.c.d.(mi , mj ) = 1 for i j. The system has a unique solution modulo M=m1m2…mr