Some fundamental Fibonacci number congruences

This paper investigates a number of congruence properties related to the coefficients of a generalized Fibonacci polynomial. This polynomial was defined to produce properties comparable with those of the standard polynomials of some special functions. Some of these properties are compared with known...

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Vydáno v:Notes on number theory and discrete mathematics Ročník 31; číslo 1; s. 27 - 40
Hlavní autoři: Shannon, Anthony G., He, Tian-Xiao, Shiue, Peter J.-S., Huang, Shen C.
Médium: Journal Article
Jazyk:angličtina
Vydáno: "Prof. Marin Drinov" Publishing House of Bulgarian Academy of Sciences 01.04.2025
Témata:
appell polynomials
congruences
fibonacci sequences
generalized fibonacci polynomials
lucas sequences
recurrence relations
special functions
ISSN:1310-5132, 2367-8275
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Popis
Shrnutí:This paper investigates a number of congruence properties related to the coefficients of a generalized Fibonacci polynomial. This polynomial was defined to produce properties comparable with those of the standard polynomials of some special functions. Some of these properties are compared with known identities, while others are seemingly characteristic of arbitrary order recurrences. These include generalizations of, and analogies for, results of Appell, Bernoulli, Euler, Hilton, Horadam and Williams. In turn, the theorems lead to conjectures for further development.
ISSN:1310-5132
2367-8275
DOI:10.7546/nntdm.2025.31.1.27-40