Take ; and

It should be

Now, the proof I've found is nasty

We have

Let's define

M divides any linear combination ( with integer coeficients) of those 2.

So M divides: i.e.

Again: Thus:

And this goes on:

We keep on eliminating terms, the idea is to have only 1 term in the end.

If is even we eventually get: ( or the symmetric)

Whereas if n is odd:

But, since M divides a-b and (a,b)=1 then and thus we must have