I really don't know how to tackle this proof because it has mod in it. There's 3 parts to the question. You don't have to answer all three parts (would be cool to check answer with though), I just need a starting point so get this proof rolling. 

Question: 

Relatively Prime: Means if two numbers' greatest common divisor is $1$.
Let $a$ and $n$ be two natural numbers. Prove that if $a$ and $n$ are relatively prime, there exists a unique natural number $b < n$ such that $ab \equiv\_n 1$ by doing the following:

a) Prove that 
$$\exists b \in \mathbb N, b < n \land ab\equiv\_n 1. \tag1$$

b) Add to equation ($1$) in part (a) to express that $b$ is unique.

c) Now prove $b$ is unique.

(If you need a picture of the question [Question picture](https://i.stack.imgur.com/KPhYe.png)