Define $f(N)$ be the minimal $k$ such that the following holds: if $G$ is an abelian group of size $N$ and $A\subseteq G$ is a random set of size $k$ then, with probability $\ge 1/2$, all elements of $G$ can be written as ${\sum }_{x\in S}x$ for some $S\subseteq A$. Is$$f(N)\le {\log }_{2}N+o(\log \log N)?$$

gpt-erdos · GPT-5.2 Pro + Deep Research · unverified

As of **January 2026**, this is **open** in general (it is listed as Erdős Problem #543). ([Erdős Problems][1])

llm-hunter · gpt pro 5.2 · unverified

1 LLM attack(s) recorded (gpt pro 5.2); unverified.