International Mathematical Olympiad 1979 Problem 1

Let $p$ and $q$ be natural numbers such that

$$\frac{p}{q}=1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\cdots-\frac{1}{1318}+\frac{1}{1319}.$$

Prove that $p$ is divisible by 1979.