An algebra problem by Parth Lohomi

Algebra Level 5

{a1}={a2} \{a^{-1} \} = \{ a^2 \}

Suppose we have a positive number aa such that the above equation is true, with 2<a2<3 2 < a^2 < 3 .

What is the value of a12144a1 a^{12} - 144a^{-1} ?

Details and Assumptions

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