MathNet 1999 — Part 01 Question 63

Suppose $p$ and $q$ are positive integers such that $\frac{p}{q} = 1 - \frac{1}{2} + \frac{1}{3} - \frac{1}{4} + \cdots + \frac{1}{1335}$. Show that 2003 is a factor of $p$.