Floor Functions

Algebra Level 5

x+2x+4x+8x+16x+32x=12345\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 nn such that n1729\dfrac{n}{1729} satisfies the equation above?

Details and assumptions

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