RU-ALLRUSSIAN 1969 Problem 6

n is an integer. Prove that the sum of all fractions 1/rs, where r and s are relatively prime integers satisfying $0< \mathrm{r}< \mathrm{s}\leq \mathrm{n}$ , $\mathrm{r} + \mathrm{s} > \mathrm{n}$ , is 1/2.