ProbXiv
sign in

Erdős Problem #848

Number theory · posed by Paul Erdős, András Sárközy, 1992 · solved

1 attempt · 1 machine check

Statement

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.

Context

Resolved for all sufficiently large N via a stability theorem; small N remain a finite computation (erdosproblems.com marks the problem DECIDABLE)

A numbered problem from the Erdos catalog: real and documented, with a specialist audience. Checked against erdosproblems.com: no prize attached and a modest reference trail, so it sits at the band's baseline.

People

begin a project on this problem →

Attempts

1 attempt

No person has examined this. There is 1 attempt here and 1 machine check recorded against it. A machine check is a judgement recorded by a tool: no account is credited for it, nobody has put their name to it, and it is not verification by a person. Saying whether the mathematics holds is the most useful thing anybody can do on this page.

review this attempt →

  • #1

    Attempt 1

    proof attemptGPT-5 with Mehtaab Sawhney, Mark Sellke ·
    AI involvement
    ai co developed
    — a person and a model developed the result together.
    models
    GPT-5
    people
    Mehtaab Sawhney, Mark Sellke

    Sawhney's note resolving the problem cites a ChatGPT (GPT-5) session in the provenance of the key lemma, and Tao's AI-contributions ledger records the solve as GPT-5 working with Sawhney and Sellke (October-November 2025).

    Resolved for all sufficiently large N via a stability theorem; small N remain a finite computation (erdosproblems.com marks the problem DECIDABLE)

    Reviews

    1 machine check

    No person has reviewed this attempt. 1 machine check below — a machine check is not human verification.

    • Machine check · not human verification

      machine: correct

      Recorded from VibeMathed site check ·

      scope Reproduction by the VibeMathed site

      erdosproblems.com marks the problem resolved up to a finite check and links Sawhney's note; no formal artifact and no journal review.

      No ProbXiv account is credited for this check. Nobody has put their name to it, so it carries no personal accountability and does not count as verification by a person.

    Discussion of this attempt

    no comments

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.

Discussion

no comments

Nothing has been said about this problem yet.

Reading every thread is open to everyone. Posting needs an account with posting rights — sign in to check yours.