# Is $$12^2$$ special?

Algebra Level 4

$\begin{cases} \{a^{-1}\}=\{a^2\} \\ 2<a^2<3 \end{cases}$

Suppose that $$a$$ is positive and satisfies the above conditions, find the value of $$a^{12}-144a^{-1}$$.

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

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