We confirm three conjectures of Guo and Zeng on Franel numbers and binomial coefficients. Furthermore, we prove more refined divisibility results for a large class of polynomial sequences.

中文翻译：

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证明弗内尔数和二项式系数的三个整除性

我们证实了郭和曾关于弗内尔数和二项式系数的三个猜想。此外，我们为一大类多项式序列证明了更精细的可分性结果。