3. (FIN 3) Does there exist a second-degree polynomial $p(x, y)$ in two variables such that every nonnegative integer $n$ equals $p(k, m)$ for one and only one ordered pair $(k, m)$ of nonnegative integers?
3. The answer: yes. Set
$$
p(k, m)=k+[1+2+\cdots+(k+m)]=\frac{(k+m)^{2}+3 k+m}{2} .
$$

It is obviously of the desired type.