# Floor Functions

Algebra Level 5

$\large \lfloor x\rfloor+\lfloor 2x\rfloor+\lfloor 4x\rfloor+\lfloor 8x\rfloor+\lfloor 16x\rfloor+\lfloor 32x\rfloor=12345$

What is the number of integral values of $$n$$ such that $$\dfrac{n}{1729}$$ satisfies the equation above?

Details and assumptions

• $$\lfloor x\rfloor$$ represents the greatest integer function.
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