First of all, given that is a whole even number, let's write for some natural . Then observe that we are allowed, according to Newton, to write
And notice that
is an even number, since the factor happens to appear in all of the terms (and this is only possible because ).
Now, this is . Adding the we get
is an odd number, since
is even (for , where ) and for all the other terms is even. Therefore
has no factors and
has all the factors in evidence. Then for an even has only one factor .