Abstract Algebra modular Arithmatic Proof

[ETuten]

Homework Statement

Prove 10ⁿ ≡₁₈ 10 for all n ϵ N

Homework Equations

I have no idea where to even begin this proof.

The Attempt at a Solution

 

[Billy Bob]

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

 

[ETuten]

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

 

[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 ____?