1. Is Z x Z cyclic? [Here Z means (Z, +).]

2. Prove the Chinese remainder theorem: If are positive integers such that and are relatively prime for i not equal to j, and are any integers, then there is an integer x such that x is congruent to for 1 less than or equal to i less than or equal to n. (Hint: Consider the generator (1,1,....,1) for X......X )