Originally Posted by DMT
Think about what happens when you expand the powers on the RHS.
Every term will be of the form:
where is an integer, and .
When is an even integer the term is an integer and when it is an odd
integer it is an integer times , so the RHSs can be writen in the form
where and are integers. Also it is obvious that
the coefficients of have equal magnitudes but opposite signs
in the two equations.