Abstract Algebra modular Arithmatic Proof

1. Apr 9, 2009

ETuten

1. The problem statement, all variables and given/known data

Prove 10n18 10 for all n ϵ N

2. Relevant equations

I have no idea where to even begin this proof.
3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Apr 9, 2009

Billy Bob

What is the definition of $$a\equiv_n b$$ ?

3. Apr 9, 2009

ETuten

it is said to be congruent integer modulo if n|a-b

4. Apr 9, 2009

Billy Bob

So apply this definition to your problem. What are you trying to show? I.e., you are trying to show ____ is divisible by ____?

What would have to be true for a number to be divisible by ____?