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Erdős problem 906

Is there an entire non-zero function f:C→Cf:\mathbb{C}\to \mathbb{C} such that, for any infinite sequence n1<n2<⋯n_1<n_2<\cdots, the set {z:f(nk)(z)=0 for some k≥1}\{ z: f^{(n_k)}(z)=0 \textrm{ for some }k\geq 1\} is everywhere dense? The literal question is trivial for polynomials, so the claims address the transcendental entire case, in the affirmative.

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No reviewed Result is current in Vela Mathematics Program. Retained source material is shown below.

Retained declaration

FormalConjectures/ErdosProblems/906.lean

Formal Conjectures

FormalConjectures/ErdosProblems/906.leanErdos906.erdos_9064 linesExact file
True ↔  ∃ f,    Transcendental (Polynomial ℂ) f ∧      Differentiable ℂ f ∧ ∀ (n : ℕ → ℕ), StrictMono n → Dense {z | ∃ k, iteratedDeriv (n k) f z = 0}
OpenStatement only, no proof

Reported activity

Work these sources record against this Problem. Source-reported attribution, not reviewed here.

  • AI collaborating with humans

    Erdős AI contributions wiki · 25 Apr, 2026

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    Adriano Almeida
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  • AI collaborating with humans

    Erdős AI contributions wiki · 25 Apr, 2026

    Machine
    GPT-5.5 Pro
    People
    Przemek Chojecki
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  • Solved as stated, hidden constraints

    GPT-Erdős

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  • argument

    VibeMathed

    Machine
    GPT-5.5 Pro
    People
    Przemysław Chojecki
    Reported outcome
    candidate
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