Function for unique hash code

Question

I am interested in finding $F(x,y)$, such that $x$ and $y$ $\in \mathbb Z^+$ and $F(x,y)$ is one to one function i.e., $F(x,y)$ is unique for any unique unordered pairs of $x$ and $y$.

Regards,

Apologies for noobish language I am new to branch of number theory.

Answer 1

$F(x,y)=(1+\max(x,y))^2-|x-y|$ will do.