IMO 1979 - Shortlisted problems Question 7

(FRG 1) IMO1. Given that $1-\frac12+\frac13-\frac14+\cdots-\frac1{1318}+\frac1{1319}=\frac pq$, where $p$ and $q$ are natural numbers having no common factor, prove that $p$ is divisible by $1979$.