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极值问题 数学

描述

K已知m、n为整数,且满足下列两个条件:

① m、n∈1,2,…,K,(1≤K≤10^9)

② (n^ 2-mn-m^2)^2=1

编一程序,对给定,求一组满足上述两个条件的m、n,并且使m^2+n^2的值最大。例如,若K=1995,则m=987,n=1597,则m、n满足条件,且可使m^2+n^2的值最大。

输入输入仅一行,K的值。输出输出仅一行,m^2+n^2的值

样例输入
1995

样例输出
3524578

 

分析:

裸Fibonacci sequence

 

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