Lagrange proved that every nonnegative integer is a sum of 4 squares.

Gauss proved that every nonnegative integer is a sum of 3 triangular numbers.

Is there a 2-variable polynomial $f(x,y) \in \mathbf{Q}[x,y]$ such that $f(\mathbf{Z} \times \mathbf{Z})=\mathbf{N}$?