Long Time No See - Coming Back With High-ordered Questions

Algebra Level 4

Let \(a\) be a positive number in the interval \(2<a^2 <3 \) and it satisfy the equation \(\left \{ \dfrac{1}{a} \right \} = \{a^2 \} \).

Find the value of \(a^{12} - 144a^{-1}\).

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Notation: \( \{ \cdot \} \) denotes the fractional part function.

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