小弟帮 Livar 兄贴:
B40:
Let S = summation/ sum of
(1) Sx = 1999
(2) Sx^4 = Sx^3
(2) - (1) : S (x^4-x) = Sx^3-1999 = S(x^3-1)
hence
Sx(x^3-1)=S(x^3-1)
S(x-1)(x^3-1)=0
S(x-1)^2(x^2+x+1)=0
It's easy to determine x^2+x+1>0
hence the only solution is
every x = 1.
Which is X_1=X_2=X_3=...=X_1999=1