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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