Originally Posted byDMT

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.

RonL