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Erdős problem 848

Is the maximum size of a set A⊆{1,…,N}A\subseteq \{1,\ldots,N\} such that ab+1ab+1 is never squarefree (for all a,b∈Aa,b\in A) achieved by taking those n≡7(mod25)n\equiv 7\pmod{25}? Resolved for all sufficiently large NN: any near-maximal AA is contained in {n≡7(mod25)}\{n\equiv 7\pmod{25}\} or {n≡18(mod25)}\{n\equiv 18\pmod{25}\}, leaving only a finite check.

No current result

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

Retained declaration

FormalConjectures/ErdosProblems/848.lean

Formal Conjectures

FormalConjectures/ErdosProblems/848.leanErdos848.erdos_8481 lineExact file
True ↔ ∀ (N : ℕ), Erdos848.Erdos848For N
SolvedStatement 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 · 12-15 Mar, 2026

    Machine
    Claude Opus 4.6, GPT-5.4
    People
    Malek Zribi
    Open the source record

  • AI building on literature

    Erdős AI contributions wiki · 5-23 Mar, 2026

    Machine
    Gemini 3.1 Pro, GPT-5.2 Thinking, GPT-5.4 Thinking
    Open the source record

  • AI collaborating with humans

    Erdős AI contributions wiki · 12 Oct-20 Nov, 2025

    Machine
    GPT-5
    People
    Mehtaab Sawhney, Mark Sellke
    Open the source record

  • Formalization

    Erdős AI contributions wiki · 28 Jan, 2026

    Machine
    Aristotle, Claude, GPT-5.2
    Open the source record

  • argument

    VibeMathed

    Machine
    GPT-5
    People
    Mehtaab Sawhney, Mark Sellke
    Reported outcome
    resolved
    Open the source record

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