Problem 531

Erdős Problem #531: declared status 'open'. Formalized: no. Let $F(k)$ be the minimal $N$ such that if we two-colour $\{1,\ldots,N\}$ there is a set $A$ of size $k$ such that all subset sums $\sum_{a\in S}a$ (for $\emptyset\neq S\subseteq A$) are monochromatic. Estimate $F(k)$. Current best: Balogh, Eberhrad, Narayanan, Treglown, and Wagner [BENTW17] have improved this to$$F(k) \geq 2^{2^{k-1}/k}.$$ References [BENTW17] Balogh, J\'{o}zsef and Eberhard, Sean and Narayanan, Bhargav and Treglown, Andrew and Wagner, Adam Zsolt, An improved lower bound for Folkman's theorem. Prize: no. Tags: number theory, ramsey theory.