Question 9Find the number of cubic polynomials $p(x) = x^3 + ax^2 + bx + c,$ where $a,$ $b,$ and $c$ are integers in $\{-20, -19, -18, \ldots, 18, 19, 20\},$ such that there is a unique integer $m \ne 2$ with $p(m) = p(2).$