I have an infinite set of points in $\mathbb{R}^2$ given by $\{ (n, m) \}$ where $n,m \in \mathbb{N}$. The Euclidean distance of these points to the origin is given by $\sqrt{n^2+m^2}$. My question now is, since I know that $n^2+m^2 \in \mathbb{N}$ and I know that there exists multiple bijections between $\mathbb{N}$ and $\mathbb{N}^2$. Is it possible to label this set of points by a single natural number, $k$, such that
$\sqrt{k} = \sqrt{n^2+m^2}$
There is a sort of bijection between using the label $k$ and the $(n, m)$ coordinates meaning: i) given a $k$, you can find associated $(n, m)$ and the same in reverse ii) $k$ takes on all values in $\mathbb{N}$
Thanks for the help and if something is not clear let me know.