Question 99
Let $P(x)$ be a polynomial with integer coefficients and degree $n\le10$ such that for each $k\in\{1,2,\ldots,10\}$ there is an integer $m$ with $P(m)=k$. Also $|P(10)-P(0)|\lt 1000$. Prove that for every integer $k$ there is an integer $m$ with $P(m)=k$.