Problem 356

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.


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。

:$\lfloor a \rfloor$表示下取整函数。