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Largest roots of cubic polynomials

Problem 356

Published on Saturday, 29th October 2011, 01:00 pm; Solved by 333

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.

Note: represents the floor function.