For all real numbers , let be a function with fundamental period .
Let . If can be expressed as , where and are positive integers with coprime and square-free, find .
For all integers , we define as follows: For all , let Find .
Details and assumptions
As an explicit example, since , , whereas since . Note that .
The floor function denotes the largest integer less than or equal to . For example, .
You might use a scientific calculator for this problem.
Find for .
Clarifications:
denotes the derivative of .
denotes the factorial notation. For example, .