Total number of values of

MATHEMATICS · Single correct · AoPS · Mathematics · Special Functions · Special Functions

Problem

x

, of the form

\frac{1}{n}

n \in N

in the interval

x \in \left[\frac{1}{25}, \frac{1}{10}\right]

, which satisfy the equation

\{x\} + \{2x\} + \dots + \{12x\} = 78x

(where

\{\cdot\}

represents fractional part function), is (1) 12 (2) 13 (3) 14 (4) 15