ProbXiv
sign in
Problem archiveProblem record

Erdos's Question on Shifted Pairwise-Coprime Reciprocal Sums

Number theory · posed by Paul Erdos · partial

1 comment

Statement

Let M(n)\mathcal{M}(n) be the supremum of ∑a∈A1/(n−a)\sum_{a \in A} 1/(n-a) over pairwise coprime A⊂[1,n)A \subset [1,n). Erdos asked whether M(n)≤∑p<n1/p+O(1)\mathcal{M}(n) \le \sum_{p<n} 1/p + O(1) uniformly. The average order is settled: ∑n≤NM(n)=e−γNlog⁡log⁡N+O(N)\sum_{n \le N} \mathcal{M}(n) = e^{-\gamma} N \log\log N + O(N).

Record

Source
Added

Comments

No person has examined this. Nothing here has been checked at all. say whether it holds →

  1. proof attempt · #1

    Eric Li, using ChatGPT

    That credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.

    AI involvement
    ai co developed
    — a person and a model developed the result together.

    The declaration says ChatGPT was used for ideation and formalization during preparation, with the author responsible for the mathematics. Part of the same series of Erdos-problem resolutions in this catalog.

    the average order; the uniform bound Erdos asked about is not settled

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.