A note on a question of Erdős (Q1379600)

The author deduces the following result from Ramsey's theorem: If the set of positive integers is split into \( r \) classes, then at least one of these classes contains three distinct integers \( x, y, z \), satisfying \({1 \over x} + {1 \over y} = {1 \over z} \). He also refers to the work of Lefmann and Brown and Rödl on this problem of combinatorial number theory, which was posed by P. Erdős.