Fibonacci数与Lucas数平方组合的一组恒等式

A Group of Identities of Squared Combination of Fibonacci Number and Lucas Number

目的研究Fibonacci数与Lucas数平方组合的计算公式.方法初等方法.结果得到了关于Fibonacci数与Lucas数平方组合的一组恒等式,同时得到了Fibonacci数与Lucas数平方和与差以及Fibonacci数平方、Lucas数平方的计算公式.结论此方法将被用于其他数列的研究,并为Fibonacci数与Lucas数的研究提供了新的思路。

Aim To study the calculating formula of squared combination of Fibonacci number and Lucas number.Method Primary method. Result A group of identities of squared combination of Fibonacci number and Lucas number is obtained. Meanwhile the squared sum and difference of Fibonacci number and Lucas number, together with the calculating formula for square of Fibonacci number and Lucas number, is obtained. Conclusion This method can be used in the study of other number series, and provide new way for the study of Fibonacci number and Lucas number.