Problem 774

Erdős Problem #774: declared status 'open'. Formalized: yes. We call $A\subset \mathbb{N}$ dissociated if $\sum_{n\in X}n\neq \sum_{m\in Y}m$ for all finite $X,Y\subset A$ with $X\neq Y$. Let $A\subset \mathbb{N}$ be an infinite set. We call $A$ proportionately dissociated if every finite $B\subset A$ contains a dissociated set of size $\gg \lvert B\rvert$. Is every proportionately dissociated set the union of a finite number of dissociated sets? Prize: no. Tags: number theory.