中文摘要：

Lucas数列{Ln}的模数列是纯周期数列。本文根据模数列的定义,利用初等数论的知识,讨论Lucas数列的模数列的周期性的一个性质,证明：当m1,m2是不同的正整数时,Lucas数列的模数列{bn（m1）}和{bn（m2）}的最小正周期分别是T1,T2,则模数列{bn[m1,m2]}的最小正周期为[T1,T2]。

英文摘要：

The Modular Sequence of Lucas Sequence is the periodic sequence as well as a simple periodic sequence. According to the definition of modular sequence, we discussed a character of the period of modular sequence of Lucas sequence and obtained a prop-erty ：If m1 and m2 are different positive integers, and the least positive periods of the modular sequence {（bn（mj）} and {bn（ m2） of Lu-cas sequence Ln are T1 and T2 respectively, then the least positive period of the modular sequence { bn[m2 ,m2]}is T1 ,T 2.