Open AccessDivisibility of Fibonomial coefficients in terms of their digital representations and applications
Author(s) -
Phakhinkon Phunphayap,
AUTHOR_ID,
Prapanpong Pongsriiam
Publication year - 2022
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
ISSN - 2473-6988
DOI - 10.3934/math.2022296
Subject(s) - divisibility rule , mathematics , prime (order theory) , combinatorics , characterization (materials science) , arithmetic , discrete mathematics , physics , optics
We give a characterization for the integers $ n \geq 1 $ such that the Fibonomial coefficient $ {pn \choose n}_F $ is divisible by $ p $ for any prime $ p \neq 2, 5 $. Then we use it to calculate asymptotic formulas for the number of positive integers $ n \leq x $ such that $ p \mid {pn \choose n}_F $. This completes the study on this problem for all primes $ p $.