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first 200 decimal digits of a^2000, cubic (VII Soros Olympiad 2000-01 R1 11.4)

Source:

July 29, 2021

number theoryDigits

Problem Statement

Let

a

be the largest root of the equation

x^3 - 3x^2 + 1 = 0

. Find the first

200

decimal digits for the number

a^{2000}