Some Properties of Fibonacci Numbers, Generalized Fibonacci Numbers and Generalized Fibonacci Polynomial Sequences

摘要

In this paper we study the Fibonacci numbers and derive some interestingproperties and recurrence relations. We prove some charecterizations for $F_p$,where $p$ is a prime of a certain type. We also define period of a Fibonaccisequence modulo an integer, $m$ and derive certain interesting propertiesrelated to them. Afterwards, we derive some new properties of a class ofgeneralized Fibonacci numbers. In the last part of the paper we introduce somegeneralized Fibonacci polynomial sequences and we derive some results relatedto them.