Problem detail · source-aware
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Ross introduced $\mathcal{S}$-perfect numbers, integers expressible as $1 + \sum \lambda_j d_j$ over their proper divisors with coefficients in $\mathcal{S}$, and conjectured that they have the same density as the nondeficient numbers, plus a second conjecture relating odd nondeficient numbers to $\mathcal{S}$-perfection. Both are false.
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The paper says in its introduction that the disproofs are built on extensive interactions with GPT-5.5 Pro, and the acknowledgements place that interaction in the exploratory and proof-development stages. All AI suggestions were substantially revised, corrected and independently verified by the author.
Provider: OpenAI · Prompt public: unknown · Independence: unknown
Single-author arXiv preprint; not yet peer-reviewed.
Correctness: unknown · statement fidelity: unaudited · peer review: none
VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Source-reported tools: argument.
Independent: unknown · difference confidence: 0
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.