Thread: Modular Proofs

I just can't seem to grasp modular arithmatic and I am trying to solve a few simple proofs:

* means "is congruent"

1) Prove if [m * n (mod 7)] then [m * N (mod 14)]

2) Prove if [3 | n] then [n^(2) * 1 (mod 3)]

Also does anyone know any good sites with some basic proofs like these with solutions? Any help is appreciated.

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.

1) Prove if [m * n (mod 7)] then [m * N (mod 14)]

What is N? Does n=N?

2) Prove if [3 | n] then [n^(2) * 1 (mod 3)]

This statement is false. Counterexample: For , . But