ProbXiv
sign in
Problem archiveProblem record

Erdős Problem #942

Number theory · posed by 1976 · partial

2 comments

Statement

Let h(n)h(n) count powerful integers in [n2,(n+1)2)[n^2, (n+1)^2). What is the extremal order of h(n)h(n)?

Record

Source
Added

Comments

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

  1. proof attempt · #1

    Claude, Codex, Aristotle

    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.

    lower bound improved to ≫ log n/(log log n · log log log n) infinitely often; the extremal order remains open

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

    lean: correctLean

    scope Lean formalization of the result

    Lean-checked.

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

Sign in with an institutional address to take part in the discussion. Reading every thread stays open to everyone.

Sign in

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.