Prove that if $$\frac{p}{q}=1-\frac{1}{2} + \frac{1}{3}- \frac{1}{4} + ... -\frac{1}{1334} + \frac{1}{1335}$$where $p, q \in Z_+$ then $p$ is divisible by $2003$.
Source: 2003 Cuba MO 2.2
Tags: number theory, divides
Prove that if $$\frac{p}{q}=1-\frac{1}{2} + \frac{1}{3}- \frac{1}{4} + ... -\frac{1}{1334} + \frac{1}{1335}$$where $p, q \in Z_+$ then $p$ is divisible by $2003$.