Let $f (n)$ be the maximal $k$ such that in any set $A \subset R$ of size $n$ there is a subset $B \subseteq A$ of size $∣ B ∣ \geq k$ which is dissociated that is, the sums $\sum_{b \in S} b$ are distinct for all $S \subseteq B$ . Estimate $f (n)$ - in particular, is it true that $f (n) \geq ⌊ lo g_{2} n ⌋?$

Worked, still open.

number theory · open · possible · 0 attempts

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vela registry pull vfr_37aec80d874a0239

vela reproduce examples/erdos-problems

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unverified AI candidates (2)

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

[ d(A):=\max{|B|:B\subseteq A\text{ is dissociated}}, \qquad f(n):=\min_{|A|=n} d(A). ]

llm-hunter · gpt pro 5.2 · unverified

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

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