With $A \subseteq \mathbb{N}$, given that

> 
> A1. $(x \in A \land y \in A) \implies x^2 + y ^2 \in A$
> 
> 
> A2. $1 \in A$
> 
> 
> A3. $3 \notin A$
> 
> 
> 

Determine whether:

> 
> $18 \notin A$
> 
> 
> 

I've been unable to prove this. First, I tried to demonstrate $18 \in A$, but no matter what I try, I can't land in $18$, so I guess that $18 \notin A$ should be true - but how can I prove it? I have never used $3 \notin A$, which is probably the key, but I'm not sure how.