# You Can't Get An Equation Shorter Than This.

Algebra Level 5

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 $$\{x\}=x-\left\lfloor x\right\rfloor$$.

×