Explicit formulas for the $p$-adic valuations of Fibonomial coefficients II
Copyright policy )Explicit formulas for the $p$-adic valuations of Fibonomial coefficients II
In this article, we give explicit formulas for the $p$-adic valuations of the Fibonomial coefficients ${p^a n \choose n}_F$ 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 ${pn \choose n}_F$ is divisible by $p$, where $p$ is any prime which is congruent to $\pm 2 \pmod{5}$.
updated and submitted
- Silpakorn University Thailand
Prime Number Theory and L-Functions, fibonomial coefficient, Arithmetic of Multiple Zeta Values and Related Functions, fibonacci number, \(p\)-adic valuation, Algebraic Geometry and Moduli Theory, Prime (order theory), QA1-939, FOS: Mathematics, binomial coefficient, divisibility, Number Theory (math.NT), \(p\)-adic order, Algebra and Number Theory, Mathematics - Number Theory, Arithmetic, 11B39, 11B65, 11A63, Fibonacci number, Continuation, Discrete mathematics, $p$-adic order, Computer science, Programming language, Ramanujan-Type Formulas, Binomial coefficients; factorials; \(q\)-identities, Combinatorics, Physical Sciences, $p$-adic valuation, Fibonacci and Lucas numbers and polynomials and generalizations, Geometry and Topology, Mathematics
Prime Number Theory and L-Functions, fibonomial coefficient, Arithmetic of Multiple Zeta Values and Related Functions, fibonacci number, \(p\)-adic valuation, Algebraic Geometry and Moduli Theory, Prime (order theory), QA1-939, FOS: Mathematics, binomial coefficient, divisibility, Number Theory (math.NT), \(p\)-adic order, Algebra and Number Theory, Mathematics - Number Theory, Arithmetic, 11B39, 11B65, 11A63, Fibonacci number, Continuation, Discrete mathematics, $p$-adic order, Computer science, Programming language, Ramanujan-Type Formulas, Binomial coefficients; factorials; \(q\)-identities, Combinatorics, Physical Sciences, $p$-adic valuation, Fibonacci and Lucas numbers and polynomials and generalizations, Geometry and Topology, Mathematics
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