IMO 1979 Problem 1

If $p$ and $q$ are natural numbers so that $$\frac{p}{q}=1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+ \ldots -\frac{1}{1318}+\frac{1}{1319},$$ prove that $p$ is divisible with $1979$ .