Floors and Fraction

Algebra Level 5

x+2017x=x+2017xx + \dfrac {2017}{x} = \lfloor x \rfloor + \dfrac {2017}{\lfloor x \rfloor} If the sum of all non-integer real solutions xx to the above expression can be represented as ab\frac{a}{b}, where aa and bb are coprime integers and bb is positive, find a+ba+b.

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