Some Properties of Fibonacci Numbers, Generalized Fibonacci Numbers and Generalized Fibonacci Polynomial Sequences
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In this paper we study the Fibonacci numbers and derive some interesting properties 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 properties related to them. Afterwards, we derive some new properties of a class of generalized Fibonacci numbers. In the last part of the paper we introduce some generalized Fibonacci polynomial sequences and we derive some results related to them.
Abstract
In this paper we study the Fibonacci numbers and derive some interesting properties 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 properties related to them. Afterwards, we derive some new properties of a class of generalized Fibonacci numbers. In the last part of the paper we introduce some generalized Fibonacci polynomial sequences and we derive some results related to them.
참고문헌 (6)
- M. Bicknell-Johnson, "Divisibility properties of the Fibonacci numbers minus one, generalized to Cn = Cn−1 + Cn−2 + k", Fibonacci Quart, 28, pp.107~112 (1990)
- D. M. Burton, "Elementary number theory" (2007), Tata McGraw Hill
- G. B. Djordjevic, "Some generalizations of certain sequences associated with the Fibonacci numbers", J. Indones. Math. Soc, 12(1), pp.99~112 (2006)
- G. B. Djordjevic, "Some generalizations of the incomplete Fibonacci and the incomplete Lucas polynomials", Adv. Stud. Contemp. Math., 11(1), pp.11~32 (2005)
- V. E. Hoggatt, Jr., "Some congruences of the Fibonacci numbers modulo a prime p", Math. Mag., 47, pp.210~214 (1974)
- R. A. Mollin, "Fundamental number theory with applications", pp.2008, Chapman and Hall