I have read through a lot of similar posts so I am not trying to re ask a question but just seeking some clarity.
I am looking at the Pell and Pell like equations:
$x^2-2y^2=1$ and $x^2-2y^2=k$ where $k=6n+1$ for $n \in \mathbb N$. I am just curious to know if all solutions have either $x$ or $y \equiv 0 \mod 3$ $\quad$ or if I am thinking about this completely wrong.
So for a problem that I am looking at the smallest solution would be $(3,2)$ because $(1,0)$ would not make sense. So when I used the seed it gave solutions with either $x,y$ divisible by 3 but I am sure my thinking is flawed.