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MathNet 2018-part-04 — 181 problems (EN–VI) Question 39

Math Olympiad Vault · MathNet 2018-part-04 — 181 problems (EN–VI)

Question 39

Let $\alpha$ be the unique positive root of the equation
$$
x^{2018} - 11x - 24 = 0
$$
Find $\left\lfloor \alpha^{2018} \right\rfloor$. (Here, $\lfloor x\rfloor$ denotes the greatest integer less than or equal to $x$.)