Cohen's 22 Conjectures on Cyclic Numbers

Precise statement

22 conjectures of Cohen about cyclic numbers (integers with $\gcd(n, \varphi(n)) = 1$) 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).

The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement fidelity, correctness, priority, or novelty.

What AI did

GPT-5

"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.

Provider: OpenAI · Prompt public: unknown · Independence: unknown

Verification boundary

unreviewed

Paper has been retracted from arXiv

Correctness: unknown · statement fidelity: unaudited · peer review: none

Timeline

1. 2025-09-30

   arXiv

   VibeMathed reports this item as retracted. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.

Known method families

argument (source-reported)

Source-reported tools: argument.

Independent: unknown · difference confidence: 0

What remains uncertain

VibeMath has not independently audited the mathematical statement, proof, or novelty claim.

• VibeMath has not independently verified the mathematical claim.
• AI-attempt independence and training-data exposure are unknown unless explicitly documented.
• VibeMath has not independently audited the mathematical statement, proof, or novelty claim.