# 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 $$a^{12} - 144a^{-1}$$.

 

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

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