Explicit formulas for the $p$-adic valuations of Fibonomial coefficients II - Phunphayap, Phakhinkon; Pongsriiam, Prapanpong (AIMS mathematics, 2020)
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 $± 2 \pmod{5}$.