AI 中文总结
本文针对d含至少两个不同素因子时无有意义界的问题，首次给出与6互素的二项式系数数量的非平凡界，推进了例外集合规模的研究。
AI 中文摘要
Singmaster的著名结论指出，任意整数d可整除几乎所有二项式系数，对例外集合的结构与规模的研究已有数十年历史。当d为素数幂时，这类集合已被充分理解且其规模已知；但当d至少含两个不同素因子时，尚无有意义的界。本文将首次给出与6互素的二项式系数数量的非平凡界。
英文摘要
It is a well known result by Singmaster that any integer $d$ divides almost all binomial coefficients. The study of the structure and the size of the exceptional set has been of interest for many decades. In the case where $d$ is a prime power, these sets are well understood and their size is known. However, if $d$ has at least two distinct prime factors, no non-trivial bounds are known. In this paper, we will provide the first non trivial bound on the number of binomial coefficients coprime to 6.
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