You Can't Get An Equation Shorter Than This.

Algebra Level 4

If the sum of all real solutions of the equation : \[\left\{x\right\}\left\lfloor x\right\rfloor =2014 x\] can be written as \(\frac{-a}{b}\) where \(a,b\) are coprime positive integers, find \(a+b\).


Details and assumption :

\(\left\lfloor \cdot\right\rfloor \) is the floor function (the greatest integer function) and \(\{x\}=x-\left\lfloor x\right\rfloor \).

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