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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Bibliographic Details
Published in:Notes on Number Theory and Discrete Mathematics
Main Authors: Anthony G. Shannon, Tian-Xiao He, Peter J.-S. Shiue, Shen C. Huang
Format: Article
Language:English
Published: "Prof. Marin Drinov" Publishing House of Bulgarian Academy of Sciences 2025-03-01
Subjects:
congruences
recurrence relations
fibonacci sequences
lucas sequences
special functions
appell polynomials
generalized fibonacci polynomials
Online Access:https://nntdm.net/papers/nntdm-31/NNTDM-31-1-027-040.pdf
Description
Summary: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

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