Find the number of integral values of satisfying sgn ( 15 1+x^2 )= 1+ 2x

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

Problem

Find the number of integral values of

x

satisfying

\operatorname{sgn}\left(\frac{15}{1+x^2}\right)=\left\lfloor1+\{2x\}\right\rfloor,

where

\operatorname{sgn}(y)

\lfloor y\rfloor

, and

\{y\}

denote the signum function, greatest integer function, and fractional part of

y

, respectively.