# An algebra problem by Parth Lohomi

Algebra Level 4

$\{a^{-1} \} = \{ a^2 \}$

Suppose we have a positive number $$a$$ such that the above equation is true, with $$2 < a^2 < 3$$.

What is the value of $$a^{12} - 144a^{-1}$$?

Details and Assumptions

• $$\{ x \}$$ denote the fractional part of $$x$$: $$\{ x \} = x - \lfloor x \rfloor$$
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