关于Fibonacci数与Lucas数关系的探讨

Discussion on the Relationship Between Fibonacci Number and Lucas Number

首先给出了Lucas数的平方与Fibonacci数平方之间的一些关系,同时利用组合数性质,给出了Lucas数、Fibonacci数和杨辉三角之间的一个新的关系式.此外,还给出了Lucas数立方与Fibonacci数立方之间的一个关系.

Some relationships are presented between Lucas numbers' square and Fibonacci numbers' square.A new expression is obtained among Lucas series,Fibonacci series and Yang Hui triangle by using the property of combination number.In addition,the relation between 3-powers of Lucas number and Fibonacci numbers is constructed.