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anemone

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**Show ⌊a¹⁷⁸⁸⌋ and ⌊a¹⁹⁸⁸⌋ are both divisible by 17**

Let $a$ be the greatest positive root of the equation $x^3− 3x^2+ 1 = 0$.

Show that $\left\lfloor{a^{1788}}\right\rfloor$ and $\left\lfloor{a^{1988}}\right\rfloor$ are both divisible by 17.