MathDB
Fractional Parts

Source:

December 20, 2005
floor function

Problem Statement

Given a nonnegative real number x,x, let ⟨x⟩\langle x\rangle denote the fractional part of x;x; that is, ⟨x⟩=x−⌊x⌋,\langle x\rangle=x-\lfloor x\rfloor, where ⌊x⌋\lfloor x\rfloor denotes the greatest integer less than or equal to x.x. Suppose that aa is positive, ⟨a−1⟩=⟨a2⟩,\langle a^{-1}\rangle=\langle a^2\rangle, and 2<a2<3.2<a^2<3. Find the value of a12−144a−1.a^{12}-144a^{-1}.
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