Lucas数列中素因子11的指数

摘要

According to the definition of the Lucas numbers,the relationship between the index of 11 in Lucas number's standard factorization and subscript is discussed by using the knowledge of the theory of elementary number and mathematical induction,then some useful conclusions are obtained the index of the prime factor 11 in Lucas numbers Ln depends on the index of the prime factor 11 in the subscript n,the index of the prime factor 11 in Ln is l+1 when the index of the prime factor 11 in n is l.%根据Lucas数列的定义,利用初等数论的知识和数学归纳法,讨论了正Lucas数Ln的标准分解式中因子11的指数与下标n的关系,得到下列结论:Ln的标准分解式中因子11的指数取决于下标n的标准分解式中因子11的指数,即当n的标准分解式中素因子11的指数为l时,L5q的标准分解式中因子11的指数为l+1.