Question 107
Let $p(x)$ be a polynomial with integer coefficients such that $p(0)=0$ and $0\leq p(1)\leq10^7$. Given positive integers $a,b$ with $p(a)=1999$ and $p(b)=2001$, determine the possible values of $p(1)$.
(Note that $1999$ is prime.)
(Note that $1999$ is prime.)