In this article, we give explicit formulas for the $p$-adic valuations of the Fibonomial coefficients $\binom{p^a n}{n}_F$ for all primes $p$ and positive integers $a$ and $n$. This is a continuation from our previous article extending some results in the literature, which deal only with $p = 2,3,5,7$ and $a = 1$. Then we use these formulas to characterize the positive integers $n$ such that $\binom{pn}{n}_F$ is divisible by $p$, where $p$ is any prime which is congruent to $\pm 2 \pmod{5}$.

中文翻译：

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Fibonomial系数的$ p $ -adic估值的显式公式II

在本文中，我们给出了所有素数$ p $以及正整数$ a $和$ n $的斐波那契系数$ \ binom {p ^ an} {n} _F $的$ p $ -adic估值的显式公式。这是我们上一篇文章的延续，扩展了文献中的一些结果，这些结果仅涉及$ p = 2,3,5,7 $和$ a = 1 $。然后，我们使用这些公式来表征正整数$ n $，使得$ \ binom {pn} {n} _F $被$ p $整除，其中$ p $是与$ \ pm 2 \ pmod一致的任何素数{5}美元。