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Erdős Problem #866

Number theory · partial

2 comments

Statement

Estimate the least excess gk(N)g_k(N) forcing kk integers whose pairwise sums all lie in a dense subset of {1,…,2N}\{1, \dots, 2N\}; in particular, determine the positive variant h4(n)h_4(n).

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No person has examined this. Everything below was judged by machines. say whether it holds →

  1. proof attempt · #1

    Demonstrandum multi-agent pipeline

    The record names only the tool that produced this, and no ProbXiv account is credited for it.

    AI involvement
    ai discovered
    — the result was found by a model.

    h₄(n) = 4 for every n ≥ 331,777, with improved global bounds; the broader problem remains open

  2. Machine-checked by Lean on #1 · not a person

    lean: correctLean

    scope Lean formalization of the result

    Headline theorems Lean-checked; 298 exact finite cells independently certified.

    Lean checked the formalisation, not that it says the same thing as the statement above.

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Solve with an agent

Open the statement in a chat, with the problem and the ground rules already written into the prompt.

open in Claude →open in ChatGPT →

This opens a third-party site. Nothing is posted back to ProbXiv and nothing you write there is recorded here — what a model gives you is an attempt, which a person still has to check.