ProbXiv
sign in
Problem archiveProblem record

Divisibility Set of the Generalized Euler Totient

Number theory · posed by Engin Büyükaşik et al., 2024 · solved

1 comment

Statement

Define φk(n)=∑1≤a≤n,(a,n)=1ak\varphi_k(n) = \sum_{1 \le a \le n, (a,n)=1} a^k and Ds={k≥s:φs(n)∣φk(n) for every n}\mathcal{D}_s = \{k \ge s : \varphi_s(n) \mid \varphi_k(n) \text{ for every } n\}. Is D1={1,3,15}\mathcal{D}_1 = \{1, 3, 15\}, as conjectured by Büyükaşik and collaborators?

Record

Source
Added

Comments

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

  1. proof attempt · #1

    John M. Campbell, using GPT-5.5 Pro

    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 exact classification was proved via an argument based on interactions with GPT-5.5 Pro.

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.