有关卢卡斯数列的充要条件和性质研究

On the necessary and sufficient conditions and properties of Lucas sequence

对卢卡斯数列进行了一些讨论,把卢卡斯数列的通项用一个一元二次方程两个根n次方的和来表示,得到卢卡斯数列的一个充分必要条件.在此基础上经过证明,获得了卢卡斯数列的一些经典性质,同时,结合斐波那契数列,建立了卢卡斯数列与斐波那契数列性质之间的一些相互联系.

This paper discussed the Lucas series .The general formula of Lucas sequence was represented with a linear combination of two roots nth of a two order equation .We obtain a necessary and sufficient condition of general formula of Lucas sequences .On the basis of this ,we proved some classical properties of Lucas sequence .At the same time ,we discovered some connections of Fibonacci sequence and Lucas sequence .