Question 135
Let $P(X) = a_{n} X^{n} + a_{n-1} X^{n-1} + \ldots + a_{1} X + a_{0}$ be a polynomial with integer coefficients (i.e., the numbers $a_{n}, a_{n-1}, \ldots, a_{1}, a_{0}$ are integers). If $P(2000) = 2000$ and $P(2001) = 2001$, how many of the numbers $2000, 2001, 2002, 2003, 2004$ can be equal to $P(2002)$?