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On a Congruence Involving Generalized Fibonomial Coefficients.
- Source :
- P-Adic Numbers, Ultrametric Analysis & Applications; Jan2018, Vol. 10 Issue 1, p74-78, 5p
- Publication Year :
- 2018
-
Abstract
- Let ( F ) be the Fibonacci sequence. For 1 ≤ k ≤ m, the Fibonomial coefficient is defined as . In 2013, Marques, Sellers and Trojovský proved that if p is a prime number such that p ≡ ±1 (mod 5), then p∤ $${\left[ {\begin{array}{*{20}{c}} {{p^{a + 1}}} \\ {{p^a}} \end{array}} \right]_F}$$ for all integers a ≥ 1. In 2010, in particular, Kilic generalized the Fibonomial coefficients for . In this note, we generalize Marques, Sellers and Trojovský result to prove, in particular, that if p ≡ ±1 (mod 5), then $${\left[ {\begin{array}{*{20}{c}} {{p^{a + 1}}} \\ {{p^a}} \end{array}} \right]_{F,m}} \equiv 1$$ (mod p), for all a ≥ 0 and m ≥ 1. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 20700466
- Volume :
- 10
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- P-Adic Numbers, Ultrametric Analysis & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 128018129
- Full Text :
- https://doi.org/10.1134/S2070046618010053