Problem 356
Largest roots of cubic polynomials
Let an be the largest real root of a polynomial g(x) = x3 - 2n·x2 + n.
For example, a2 = 3.86619826…
Find the last eight digits of $\sum^{30}_{i=1} \lfloor a_i^{987654321} \rfloor$.
Note: $\lfloor a \rfloor$ represents the floor function.
三次多项式的最大根
记an为多项式g(x) = x3 - 2n·x2 + n的最大实根。
例如，a2 = 3.86619826…
求$\sum^{30}_{i=1} \lfloor a_i^{987654321} \rfloor$的最后8位数字。
注：$\lfloor a \rfloor$表示下取整函数。