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Erdős Problem #1038

Analysis · posed by 1958 · candidate

1 comment

Statement

Among all nonconstant monic polynomials ff whose roots lie in [−1,1][-1, 1], determine inf⁡f∣{x∈R:∣f(x)∣<1}∣\inf_f |\{x \in \mathbb{R} : |f(x)| < 1\}|.

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

  1. proof attempt · #1

    GPT-5.5 Pro

    No person is named on this work: the record names only the tool it came from, and no ProbXiv account is credited for it.

    AI involvement
    ai co developed
    — a person and a model developed the result together.

    A July 2026 manuscript by Darvas, Peng and Tao, developed with GPT-5.5 Pro, claims the exact extremal value and measure.

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