A few basic rules for ya:

(i) literally means " leaves a remainder when divided by "

(ii) Therefore, for some integer

(iii) Alternately,

(iv) The nice thing about modular arithmetic is that it follows pretty much all the same rules as regular arithmetic. For example, if then , etc. So in most simple cases, you can treat congruences ( ) like regular equations.

What is N? Does n=N?1) Prove if [m * n (mod 7)] then [m * N (mod 14)]

This statement is false. Counterexample: For , . But2) Prove if [3 | n] then [n^(2) * 1 (mod 3)]