Skip to content

Erdős problem 138

If W(k)W(k) is the least NN such that every two-colouring of {1,…,N}\{1, \dots, N\} contains a monochromatic kk-term arithmetic progression, must W(k+1)−W(k)→∞W(k+1) - W(k) \to \infty?

No current result

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

Retained declaration

FormalConjectures/ErdosProblems/138.lean

Formal Conjectures

FormalConjectures/ErdosProblems/138.leanErdos138.erdos_1381 lineExact file
True ↔ Filter.Tendsto (fun k => ↑(Erdos138.W k) ^ (1 / ↑k)) Filter.atTop Filter.atTop
OpenStatement only, no proof

Reported activity

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

  • AI standalone

    Erdős AI contributions wiki · 10 Apr, 2026

    Machine
    DeepMind prover agent
    Open the source record

  • AI collaborating with humans

    Erdős AI contributions wiki · 10 Apr, 2026

    Machine
    GPT-5.4 Thinking
    People
    Nat Sothanaphan
    Open the source record

  • argument

    VibeMathed

    Machine
    AlphaProof Nexus
    Reported outcome
    resolved
    Open the source record

Continue

Start a contributionBrowse the source filesOpen the collection entry

Search problems.science

Find a Problem, Result, source, or page