Solve , where denotes the greatest integer function and denotes fractional part of…

MATHEMATICS · Subjective · AoPS · Mathematics · Special Functions · Special Functions

Problem

Solve

\frac{1}{[x]} + \frac{1}{[2x]} = \{x\} + \frac{1}{3}

, where

[ ]

denotes the greatest integer function and

\{ \}

denotes fractional part of

x