2. Does there exist a binary quadratic polynomial $\mathrm{P}(\mathrm{x}, \mathrm{y})$, such that for a unique pair of non-negative integers $(k, m)$, every non-negative integer $\mathrm{n}$ equals $\mathrm{P}(\mathrm{k}, \mathrm{m})$)?
2. Car Factory.

Proof Let $\mathrm{P}(\mathrm{k}, \mathrm{m})=\mathrm{k}+$ (number of points below the line $\mathrm{x}+\mathrm{y}=\mathrm{k}+\mathrm{m}$), calculate the number of points $(k, m)$, where $k$ and $m$ are integers. This number is $1+2+\cdots+(k+m)=\frac{1}{2}(k+m) \cdot(1+\mathrm{k}+\mathrm{m})$.

Therefore, $P(x, y)=\left((x+y)^{2}+3 x+y\right) / 2$ is the polynomial of the required type.