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(1)若 n= 2k(偶数)(F_(n+3)~2—F_(n+1)~2)~2+(2F_(n+4)· F_n)~2+(4F_(n+2))~2=(F_(n+3)~2+F_(n+1)~2)~2. (2)若n=2k+1(奇数) (F_(n+4)~2—F_n~2)~2+(2F_(n+3)·F_(n+1))~2+(4F_(n+2))~2=(F_(n+4)~2+F_n~2)~2. 在此:F_n,F_(n+1),F_(n+2),F_(n+3),F(n+4)连续五项.