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Erdős problem 283

Let p ⁣:Z→Zp\colon \mathbb{Z} \rightarrow \mathbb{Z} be a polynomial whose leading coefficient is positive and such that there exists no d≥2d≥2 with d∣p(n)d ∣ p(n) for all n≥1n≥1. Is it true that, for all sufficiently large mm, there exist integers 1≤n1<⋯<nk1≤n_1<\dots < n_k such that 1=1n1+⋯+1nk1=\frac{1}{n_1}+\cdots+\frac{1}{n_k} and m=p(n1)+⋯+p(nk)m=p(n_1)+\cdots+p(n_k)?

No current result

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

Retained declaration

FormalConjectures/ErdosProblems/283.lean

Formal Conjectures

FormalConjectures/ErdosProblems/283.leanErdos283.erdos_2831 lineExact file
True ↔ ∀ (p : Polynomial ℤ), Erdos283.Condition p
SolvedProof has a holeformal conjecturesexternal proof

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

Proof manifests naming this Problem

  • Jayyhk Erdős Leanjayyhk:erdos:283
  • PLBY Lean proofsErdosProblems.Erdos283
  • PLBY Lean proofsErdosProblems.Erdos283b

Reported activity

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

  • Formalization

    Erdős AI contributions wiki · 28 Mar, 2026

    Machine
    Aristotle
    Open the source record

  • Formalization

    Erdős AI contributions wiki · 6 May, 2026

    Machine
    Claude Opus 4.7, GPT-5.5 Pro
    Open the source record

  • AI collaborating with humans

    Erdős AI contributions wiki · 3 May, 2026

    Machine
    GPT-5.5 Pro
    People
    Kevin Barreto, Liam Price
    Open the source record

  • argument

    VibeMathed

    Machine
    GPT-5.5 Pro
    People
    Kevin Barreto, Liam Price
    Reported outcome
    resolved
    Open the source record

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