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Non-Covering Congruence Systems over Fq[x]

Number theory · solved

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Statement

Let Dq(n)D_q(n) be the largest possible least degree of a polynomial omitted by a non-covering family of nn distinct-modulus congruence classes in Fq[x]\mathbb{F}_q[x]. What is its asymptotic size? The answer is Dq(n)=nq−1+Oq(1)D_q(n) = \frac{n}{q-1} + O_q(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

    Rongyin Wang, using ChatGPT-5.6 Sol

    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 model contributed the nested-modulus lower-bound construction and the idea of a truncated Chinese-remainder-theorem sieve for the upper bound; the author verified the arguments, added details and filled gaps.

    leading asymptotic determined up to a bounded q-dependent term

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