Let $h_{1} (n) = h (n) = n + τ (n)$ (where $τ (n)$ counts the number of divisors of $n$ ) and $h_{k} (n) = h (h_{k - 1} (n))$ . Is it true, for any $m, n$ , there exist $i$ and $j$ such that $h_{i} (m) = h_{j} (n)$ ?

Worked, still open.

number theory · open · 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

Let (h(n)=n+\tau(n)) and (h_k=h^{\circ k}) as you defined.

llm-hunter · gpt pro 5.2 · unverified

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

AMS 11 · open (literature)

theorem erdos_414 : answer(sorry) ↔ ∀ᵉ  (m > 0) (n > 0), ∃ i j, h^[i] m = h^[j] n

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