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Erdős problem 987

Clunie [Cl67] proved that there exists an infinite sequence {zν}\{z_\nu\} on the unit circle with Aν≤νA_\nu \le \nu for all ν≥1\nu \ge 1. Translating zν=e(xν)z_\nu = e(x_\nu), the natural domain of xνx_\nu is the half-open unit interval Ico 0 1\mathrm{Ico}\,0\,1, matching the original [Er64b]/[Cl67] statement (any unit complex number is allowed, including z=1z = 1, i.e. x=0x = 0).

No current result

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

Retained declaration

FormalConjectures/ErdosProblems/987.lean

Formal Conjectures

FormalConjectures/ErdosProblems/987.leanErdos987.erdos_987.parts.i1 lineExact file
True ↔ ∀ (x : ℕ → ℝ), (∀ (j : ℕ), x j ∈ Set.Ioo 0 1) → Filter.limsup (fun k => Erdos987.A x k) Filter.atTop = ⊤
SolvedProof has a holelean4external proof

The proof uses `sorry`: part of the argument is written but not proved. Lean accepts the file; it does not accept the theorem.

Reported activity

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

  • AI standalone

    Erdős AI contributions wiki · 9 Apr, 2026

    Machine
    OpenAI internal model
    Open the source record

  • argument

    VibeMathed

    Machine
    OpenAI internal model
    People
    Boris Alexeev, Moe Putterman, Mehtaab Sawhney, Mark Sellke, Gregory Valiant
    Reported outcome
    resolved
    Open the source record

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