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Ross's Two Conjectures on Nondeficient Numbers

Number theory · posed by Ross, 2024 · disproved

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Statement

Ross introduced S\mathcal{S}-perfect numbers, integers expressible as 1+∑λjdj1 + \sum \lambda_j d_j over their proper divisors with coefficients in S\mathcal{S}, and conjectured that they have the same density as the nondeficient numbers, plus a second conjecture relating odd nondeficient numbers to S\mathcal{S}-perfection. Both are false.

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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 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.

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