put and your integral equals thus
on the last integral let and get that thus
A general formula can be found for:
Note that: let ; then :
Thus: - that is to say multiplied by the coefficient of of that polynomial in there - (*)
(*) Because is for and 0 for all other integer value of .
In particular then:
- , since our answer is the number of pairs of integers (x, y) with such that , fix a valid and that determines .