Problems Section: Problems 993 - 1000

Q993 Consider
\begin{eqnarray*}
p(n)&=&a_0+a_1n+a_2n^2+\cdots+a_kn^k\ ,\\
  q(n)&=&b_0+b_1\binom{n}{1}+b_2\binom{n}{2}+\cdots+b_k\binom{n}{k}\ ,
\end{eqnarray*}