Let $h (n)$ be such that, for any set $A \subseteq N$ of size $n$ , the set ${\frac{a}{( a , b )} : a, b \in A}$ has size at least $h (n)$ . Estimate $h (n)$ .

Worked, still open.

number theory · open · possible · formalized (Lean) · 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

Write [ Q(A):=\\{\frac a{(a,b)}:\ a,b\in A\\},\qquad h(n)=\min_{|A|=n}|Q(A)|. ]

llm-hunter · gpt pro 5.2 · unverified

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

AMS 5 11 · open (literature)

theorem erdos_539 :
    (fun n ↦ (cofactorThreshold n : ℝ)) =Θ[atTop] (answer(sorry) : ℕ → ℝ)

open