It is known that the polynomial $f(n,m)=\frac{1}{2}(n+m)(n+m+1)+m$ defines bijection $\mathbb{N}\times\mathbb{N}\to\mathbb{N}$ (Put pairs of $\mathbb{N}$ into the semiinfinite matrix and count them by diagonals). Does there exist a polynomial bijection $\mathbb{Z}\times\mathbb{Z}\to\mathbb{Z}$? The question is related to the open question about polynomial bijection $\mathbb{Q}\times\mathbb{Q}\to\mathbb{Q}$ here.
