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Cohen's 22 Conjectures on Cyclic Numbers

Number theory · posed by Cohen (OEIS conjectures); Fried · retracted

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Statement

22 conjectures of Cohen about cyclic numbers (integers with gcd⁡(n,φ(n))=1\gcd(n, \varphi(n)) = 1) settled at once - 16 proved, 6 disproved - together with a complete resolution of a related OEIS problem on sequences whose running averages are Fibonacci numbers (Fried's Conjecture 2).

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

  1. proof attempt · #1

    Duc Hieu Le, using GPT-5

    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 assisted
    — a person led the work and used a model along the way.

    "All proofs in the paper were assisted by GPT-5" - a blanket credit across 22 resolutions, with no individual attribution, so the lower tier applies.

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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.