# The inoffensive floor function

Algebra Level 5

For any real number $$x$$, let $$\left\lfloor x \right\rfloor$$ represent the largest integer number less than or equal to $$x$$. If $$1< x<{ 2 }^{ 2015 }$$ and $$2^{2015}$$ is a factor of $$\left\lfloor { 2 }^{ 2015 }x \right\rfloor -\left\lfloor x \right\rfloor$$, find the exact value of the sum of two coprime numbers $$a$$ and $$b$$ if $\frac { a }{ b } =\sqrt [ 2015 ]{ \frac { \left\lfloor { 2 }^{ 2015 }x \right\rfloor -\left\lfloor x \right\rfloor }{ \left\lfloor x \right\rfloor } } .$

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