Theorem 2.1.12

Theorem 2.1.12 If gcd(n1,n2) = 1, then the pair of congruences x ≡ a (mod n1),

x≡ a (mod n2) has a unique solution x ≡ a (mod n1n2).

Definition 2.1.10 The multiplicative group of Zn is

Z*n = {a Є Zn|gcd(a, n)=1}.

In particular, if n is a prime, then Z*n = {a|1 ≤ a ≤ n - 1}.

Definition 2.1.11 The order of Z*n is defined to be the number of elements in Z*,namely |Z*n|.