IR-MO 2001 Problem 2

Does there exist a sequence $\{b_{i}\}_{i=1}^\infty$ of positive real numbers such that for each natural $m$ : $b_{m}+b_{2m}+b_{3m}+\dots=\frac1m$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.