Problem detail · source-aware
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Let $D_q(n)$ be the largest possible least degree of a polynomial omitted by a non-covering family of $n$ distinct-modulus congruence classes in $\mathbb{F}_q[x]$. What is its asymptotic size? The answer is $D_q(n) = \frac{n}{q-1} + O_q(1)$.
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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.
Provider: OpenAI · Prompt public: unknown · Independence: unknown
Author-verified arXiv preprint with theorem-specific AI attribution; relies on the known theorem that a non-covering family of n classes omits a polynomial of degree below n. Not yet peer-reviewed.
Correctness: unknown · statement fidelity: unaudited · peer review: none
leading asymptotic determined up to a bounded q-dependent term
Source-reported tools: argument.
Independent: unknown · difference confidence: 0
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.