Explicit Formulas for the p-adic Valuations of Fibonomial Coefficients\n II

2019/08/05 by Phakhinkon Phunphayap, Phunphayap, Phakhinkon, Prapanpong Pongsriiam +1
Mathematics · #11A63 #11B39 #11B65 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1908.01690

openalex publication_date 2019/08/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we give explicit formulas for the p-adic valuations of the\nFibonomial coefficients p^a n choose n_F for all primes p and positive\nintegers a and n. This is a continuation from our previous article\nextending some results in the literature, which deal only with p = 2,3,5,7\nand a = 1. Then we use these formulas to characterize the positive integers\nn such that pn choose n_F is divisible by p, where p is any prime\nwhich is congruent to \± 2 pmod5.\n

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