MathNet 2007-part-02 — 187 problems (EN–VI) Question 79

Let $p(x)=x^{20}+a_{19} x^{19}+a_{18} x^{18}+\ldots+a_{1} x+a_{0}$ be a polynomial with integer $a_{i}$. We know that, for all integers $k$ between 1 and 20, $p(k)=2 k$. What are the last 3 digits of $p(21)$ ?